Remember that he is only T5 and 4 wounds. If you manage to get a couple wounds on the DP before it gets into combat, then it has to find a low risk combat to fight and hope soul feeder luck allows it to recover some wounds before it takes enough wounds to die. Even with charmed shield, he can be vulnerable to being plinked by regular shooting or a magic missile followed by a hit by a cannon, stone thrower, or by multiple massed rbt fire in single shot roles (by dark elves and high elves). I've found that the 5+ ward save is not quite good enough for greater daemons and DPs. He is very vulnerable to lore of death spells and, if he does not have dragonbane gem or loses it, he can be vulnerable to lore of metal spells. That is one of the reasons we see the daemon prince led WoC army do well in tournaments but always seems to lose at least one game and usually two in a competitive five round tournament. (White lions, not surprisingly, can take him on quite effectively and do enoungh wounds with S6 and 4 ranks of attacks in a horde to kill him off, especially with their BOTWD giving them a 2+ ward save to daemonic attacks. He similarly struggles against skullcrushers. A lucky terrogheist can scream him down as well.) That is the problem when once invests over 500 points in a single 4 wound character. A DP can get tied up indefinitely in combat with high AS and larger cav units, monstrous infantry or monstrous cav units and can die with bad luck or some magic helping the opposing unit win. For example, I once cast mindrazor on a unit of dark riders and miasma on the DP. The unit of six dark riders they held up and then almost killed off the DP that way; a mindrazor on the spearmen finished him off after the dark riders broke and the DP overran into that unit with the combat starting in my turn allowing me to recast mindrazor. Also, doubling as a lore of death caster, he sometimes blows himself up or takes wounds from miscasts and he will sometimes miscast in order to get purple sun off against a TG unit with a slann and skink priest with scroll or cube providing good magic defense to overcome. Always remember that if he takes enough wounds fast enough in combat he dies before soul feeder kicks in and saves him, especially if in combat with something that is not vulnerable to thunder stomp or if he rolls poorly on thunderstomp.
For LM: High Magic can be very effective and is under-rated. Arcane unforging does a lot if successful. If you take the dragonbane gem off, then roll ia High magic spell you just cast into the signature lore of metal spell and hit him with the lore of metal spell. Even peeling off the charmed shield puts him at 2+ As instead of 1+ and gives him a wound almost 2/3's of the time. Take a lore of death spell if he still has the gem up. (The lore attibute is you get to choose to forget the spell and roll for a common magic spell at the end on the magic phase, so you know what arcane unforging did.) Both the lore of death and lore of metal direct damage spells and arcane unforging can be cast out of combat at something not in combat, especially with a skink priest used for the slann, and are good against many of the high AS (but often lower LD8 or less) WoC units and characters (skullcrushers being the nastiest). It is not clear whether some of the chaos mutations and powers he takes are magic items that can be taken (some chaos mutations are magic items but others are just abilities given to the model), so that may mean you either get the dargonbane gem or the charmed shield off the DP.
A well-kitted oldblood or scar vet, especially on a cold one, with a great weapon is a big threat, especially with TG. It is his high WS combined with Daemon of Nurgle giving him -1 to be hit that makes him so nasty (often being hit on only 6's on rolls to hit) combined with having thunderstomp and being unbreakable and having a 1+ AS and 5+ ward save. Remember also that, unless supported by another unit, the DP must accept a challenge and you can hold him off and limit the damage accordingly. Also, LM armies have to deal with the DP's ability to cast purple sun and the other death spells while in combat (target units not in combat with direct damage spells. The key is to prevent the DP from recovering wounds with soul feeder at the end of each combat phase by rolling a D6 for each unsaved wound he caused in combat and recovering a wound on a 6. The DP needs to rack up a lot of wounds to get enough 6's to save him if in prolonged combat with something S5 or greater that can hit it on 5"s or better.
Hand of glory to get the WS up to 5 on TG or saurus and boost the I to reduce the potential damage from a purplse sun can be the difference in combat with a bit of luck. Also, rolling a High Magic spell into miama to cut down a bit the WS of the DP to hit it on 5's instead of 6's in combat is very important. Rolling into earthblood for the lore of life attribute and 5+ regen helps the unit stay alive longer and limits the damage and can restore a wound on a character in a challenge with the DP. If he gets into a fight with an oldblood or scar vet on cold one, apotheosis can be a pain to deal with for him as well as long as the DP does not kill the character before you get to recover wounds. The cold one mount makes the character immune to being stomped and limits the DP to its base 5 attacks. The DP will hit on 3's and wound on 3's but you get a 4+ AS and a 4+ ward save and/or a re-rollable 4+ AS to avoid wounds from the S6 attacks. That means you will often only suffer just under a wound per round of combat with a scar vet or oldblood on a cold one in combat with the DP (assuming the breath weapon has been used or spent). A great weapon, since you will be striking second anyway, at S7 really cuts through his armour and wounds him on 2's with only a 5+ AS and a 5+ ward save.
Math: T5 oldblood with 1+ AS and 4+ ward and great weapon on cold one. DP with flaming breath weapon used will cause on average 0.19 wounds one time with the breath. 5 S6 attacks hitting on 3's and wounding on 3's will cause only 0.55 unsaved wounds (with 1+ AS re-rollable or 1+ As and 4+ ward save). If on foot, the DP thunderstomp on the character will do another 0.583 wounds on average in the challenge. That means, as worst, the character takes 1.33 unsaved wounds in the first round of combat with the DP in a challenge if on foot. The oldblood with 5 attacks hits back on 5"s but wounds on 2's. with the DP having a modified 5+ As and 5+ ward save, which produces only 0.617 unsaved wounds on the DP. A cold one hits on 6's and wounds on 5's, so it does very little (0.12 average wounds per round of combat) to help out other than making the oldblood immune to terrorr and stomps. Note that an oldblood on cold one after the breath weapon is spent takes on average only 0.556 wounds while the DP takes on average 0.617 wounds per round of combat. However, with wildform on the oldblood the oldblood takes only 0.41 wounds from the DP from regular attacks and, if on foot, 0.4375 wounds from thunderstomp on average and does on average 0.77 wounds to the DP. Similarly, OTS on the oldblood raises the wound rate from 0.617 up to 0.82 per turn on the DP. If you somehow get off hand of glory on the oldblood and miasma on the DP, you will most of the time flip the WS advantage a lot to hitting on 4's instead of 5's and being hit of 4's instead of 3's, then the oldblood on cold one suffers only 0.333 wounds per round from the DP and does in response 0.926 wounds on the DP. A scar vet on cold one gets one less attack, so you need to cut the rate of wounds on the DP to 80% of above, but a scar vet on cold one with a charge on a DP and in range of the BSB can in theory hold off a DP for an averae three to four rounds of combat and puts one or two wounds on the DP and can win out with a bit of magic help to recover wounds or tip the scales a bit (by increasing S or T; it is a bit harder to tip the WS advantage enough to favor the scar vet). If that pins, the DP to a fixed position, allowing a TG charge into the flank to finish him off in a couple of turns or to keep purple sun from hitting the saurus and TG, then it is ofen worthwhile with the WoC having a lower model count. Little things like taking off charmed shield with arcane unforging or having put a couple of wounds on the DP already are just enough to turn the odds to the scar vet on cold one.
Don't underestimate the value of a lvl 2 skink priest with cube or scroll to stop purple sun one time and add to the equation. A lvl 2 beasts skink priest with amber spear can six dice the boosted version and one boosted amber spear can end the DP or so seriously wound it that it is far less scary if you have picked off the charmed shield benefit with a prior hit first. A wildform to boost of +1S and +1T of on character in challenge (and on TG or saurus) reduces the wounds the character will take and increases the ability to cut through the high AS, or better yet a savage beast of horrors (+3 A with +3 S will allow a scar vet or oldblood to cut through the AS and wound on 2+) or pann's pelt on the character (+3T ) means that the DP could be wounding a scar vet or oldblood only on a 6's will really alter the challenge combat with the DP. So a simple lvl 2 skink priest with beasts gives you a lot of potential for getting something off to help deal with the DP and the other high AS units in the WoC army. Plus amber spear is -1 to cast due to the DP being a monster\, so with a good winds of magic phase, you may force through something on the DP with arcane unforging and amber spear in your spell options.