But if we go 2h we don't need War Caster to cast shield. So If we took 1 level dip in Hexblade as Variant Human we could end up with PAM, RES (CON), +2 STR, +2 STR and be able to cast Shield as reaction to give us that extra AC between turns when we go full ham. Assuming Plate, that would be 23 AC between turns and we mostly need like 2-3 turns to burn down boss. And we only use 1st level slots of Shield anyway. Plate +1 (which should not be issue in late levels) = 24 AC. It does cost resources though but GWF with Smite rerolls would make up for it with damage spikes.
Taking War Caster faster on Half-Elf would delay either PAM or Elven Accuracy which seems like bad idea if we want to maximize damage. We could take War Caster at level 12 but it's little shame to not get that 20 CHA at 12 level.
One more thing that I got in mind: if we took Sentinel as V-human then assuming we land OA on enemy boss we can lock him down and if it has 5 feet reach, we can get in, attack fully, get back, force another OA with 0 speed lock down. Which, passively, increases our defense greatly as boss in totally unable to attack us in melee.
There's a little bit of apples vs oranges here, jumping between Human and Half-Elf analysis.
For a VHuman STR 2h build, indeed you can splash warlock (not necessarily hexblade, but hexblade is the best for various reasons) in somewhere and get the 1st level benefits, War Caster not warranted. It's just a Warlock dip late in an otherwise standard 'pure' paladin build. Comparing it with a STR 1h PAM wielder, the better option for the latter I'd say is to not deviate from their Paladin progression, in which case at the point the 2h PAM paladin is obtaining their Hexblade benefits, the 1h PAM guy is getting 4th level spells (Greater Find Steed, Death Ward) and is on a faster track towards Soul of Vengeance.
Additionally, if we're going by same item availability, the GWF 2h Hexadin above is 19 AC with 24 AC conditional at the cost of their reaction. A 1h PAM wielder would be 22 AC flat (18 plate with +2 shield), and their reaction is always free to be used for additional attacks every round (significant in large battles, as we approach Soul of Vengeance, or if you took Sentinel). There's pros and cons to each set up.
That said, reiterating the point from my previous post, if the DM allows GWF to apply to every damage die then that's
a lot of damage of higher levels. I can certainly see the appeal.
Now, a Half-Elf Hexadin is kind of a different a different animal - the core idea of the build is to exploit the CHA synergy and Elven Accuracy, and it's a multi-class through and through, not really coming into its own until late in the character progression. Compared to the Human builds above, by 13 it's going to end up with overall better racials, saves, DCs, better ranged attack, and conditional AC (as per the rarity example, 22+5). To maximize it the stat array is somewhat different too, and results in worse early levels, but that's just the way the cookie crumbles. You can make compelling cases for either maxing CHA at 12 or grabbing War Caster, but nevertheless CHA Hexadin requires War Caster to get the most juice out of the multiclass.
About dancing with Sentinel and Relentless Avenger, that's what I was referring to with lockdown. As FR said it'll not always apply, though rather than just on bosses, it also works in more general combat when an enemy moves into you out of reach of your allies. And a Half-Elf (through racial cantrip) or Hexadin can do something similar with War Caster and Booming Blade rather than with Sentinel.
Sentinel in general though is a good source of extra attacks, which in many real-world cases will result in higher overall damage delivered over a fight than a +MOD ASI.
If I'm playing from level 1+ and wanting a good damage dealer I'm choosing variant human with PAM level 1 feat, a spear and shield with the duelist fighting style. I'd make sure to start with 15 or 16 str and 16 cha.
I'd take Inspiring leader at level 4 if I had 16 str and Heavy armor master if I had 15 str. I'd stay in Paladin till level 11. I'd use my level 8 feat to increase charisma. After paladin 11 I'd dip 1 level into hexblade. I'd then take level 12 paladin to finish maxing charisma. Most of my spell slots would go toward smites.
I feel this provides one of the best and smoothest combination of offensive, defensive and out of combat progression for the paladin.
For the half-elf I would go for 16 str 16 cha starting. I would then take pam at level 4 and boost charisma at level 8 and level 12. I'd take a dip in hexblade after 11 levels of paladin.
I think the human build is better as it comes online faster and provides a good spot to take inspiring leader. Darkvision and +2 skills is nice on the half-elf though.
Similar sentiments here, but I feel Paladin too feat-starved to take Inspiring Leader.
My personal set up would be:
VHuman
16 10 13 8 10 16
1. PAM
4. RES (CON)
Going Vengeance and Dueling FS, then what to do after depends on the game.
If I want to have fun and the DM is running battle maps, and the party comp lends itself towards it, I'd grab Sentinel at 8. After that (or otherwise), it depends on whether I feel it's more important for this party to burn down enemies quickly, or to pass cancer saves. You know, what's giving us more headaches. If I want more damage STR, else CHA first - or also if I'm confident I can get Gauntlets or Belts, in which case there's no reason to spend on STR at all.
Overall, though, passing saves is really important when you're running into nasty incapacitating effects, so it's hard to overvalue it, and consequently I find it hard to justify other picks.
HAM is cool early on but it loses its luster later as you start running into attacks that chunk you for 20+ damage each and magical effects; the best defense there is to avoid the damage altogether, and as benny89 mentioned, it requires an uneven STR stat to be really worth it even then.
Mounted Combatant I really want to like but a) it's to a degree campaign dependent, and more importantly b) the
vast majority of scary enemies are Large or larger. Evasion on mount is nice, but attack substitution is dubious when a mount should be Disengaging or Dodging every turn anyways. Weighting all that, I'd rather have more Charisma.
I think that's the breadth of Paladin opportunity cost analysis in a nutshell. "Do I want more Damage, or do I want to pass Saves?"