Paladin 3 Inquisitor feels sort of lacking in terms of sustained dps. The problem is, you have very strong burst damage from wheel + conviction + god smash + smite but very little AoE and number of offensive skills to keep a steady sustained dps rotation. Once wheel is on cooldown, you barely have other good sources of dps.
Monk 3 has more constant dps and that can be reasonably high given you have high ping / decent DEX to spam double punch during your rotation cooldown. The AoE is lackluster (when compared to magic priests such as PD2 or Sadhu 3) but the damage can be quite strong against single targets such as bosses.
Comparing the two builds just in terms of dps is sort of unfair, though. Monk is straight out dps class while Paladin is hybrid between dps and support.
Barrier is, by many, considered the best support skill of Paladins. But as for myself, I believe Barrier is still pretty situational and sometimes may muddle the party (i.e. spread mobs away from AoE spells). In my opinion Resist Elements is still the best support skill Paladins have without any downsides to it. Remember 90% or more of the mobs in game have elemental attacks as their normal attacks so resist element will mitigate most common mobs damage.
With that being said, build your Paladin with the mindset of wanting a support character. Taking Monk 1 into that build would give you very marginal dps potential in comparison to supportiveness potential you could be getting from other classes.
The biggest issue with those two classes is the lack of other physical cleric classes to synergize with. Monk circles sort of overlap Paladin so it’s difficult taking both together. Taking Priest with a Paladin 3 build is not a terrible idea but the stats to increase will be conflicting. Priests revolve around having high SPR while Paladins gain very little from SPR and will deal very very little damage without STR (considering your transcended wep isn’t stage 5+ because that’s when STR stops mattering so much). Without a transcended weapon your damage will be about 30% of the damage of a full STR Paladin.
As a final comment, I’d like to emphatize the fact your healing capability will be much inferior to any other SPR/INT cleric if you go a STR/DEX Cleric 2 physical build. In most cases that won’t be much of an issue because mobs hit quite weak. But if you’re hunting a field boss or something more challenging, be prepared to feel like you can’t keep your party alive being the only main healer.