@FriendOfAFriend: I'd say Paladin does a better job at not dying though.
Paladin's Shield skill should be better, except for Magic-using monsters, which are a huge minority.
Lava Fountain is the better stun due to multiple hits. (But otherwise fairly identical) Pyromancer has a secondary 1-turn stun, which is nice
Paladin's Blind can very easily be cycled (and against undead, it's more effective, not that I'm really taking that into account), while Pyromancer has the better effect.
Paladin also has a loop that gives you over 100 Darkness resist if you have proper equipment.
Overall, I'm not sure which is better in that regard, but that's not the main point here, which is, of course, healing.
Pyromancer has a weak HP/Mana heal. 300% weapon damage for HP, 100% weapon damage for mana. That's honestly not all that great. At max levels, that's what, 300 HP and 100 Mana? Where if survival is your goal, you probably have like, 3000 HP and 1700 Mana or something. It's really great for low End builds though, but that's not here, I believe. The cooldown is also 16 turns which is a lot.
In addition, Pyromancer has a full heal for both HP and Mana every 35 turns, which is what makes it so unkillable.
Paladin has a weak heal (7%, so ~210 HP at 3000 HP) every 8 turns, 15% heal (~450) every 14 turns, and a 11% (~187?) mana heal every 12 turns. In addition, an increasing passive heal every turn, and after 20 turns, it'll always have 3% (~90) healing every turn. I can't stress how insane this is, for the record.
In addition to THAT, a full heal (at the cost of all mana, but with careful planning, all the healing, including the trinket can be kept up indefinitely) every 20 turns.
The only thing Pyromancer really has over Paladin in this regard is the fact that it regains all mana, so it has a few specific cases, like mana-stealing monsters where it's superior.
But all the same, there are specific scenarios Pyromancer can't really handle. Given an monster with enough offensive power, especially one that can't be defended against can overwhelm Pyromancer. Paladin may still be able to steel through it.
In a similar way, I'd rank Paladin as the 2nd strongest armor in the game. Of course, for most players, it's not exactly the most fun way to play, so stuff like Ascendant with it's insane damage output is going to at least FEEL better, because you never need an unkillable death machine on legs in standard play.