Well at levels 1-4 they kind of do. They do a good bit more damage than Fighters, Rogues, and barbarians.... and that's before you include flurry.
They can't take a hit, but they certainly dish it out (see my previous posts where I ran through all the numbers).
Ehhh.... On a lark, I ran a side by side comparison of all three Monk subclasses compared to a Champion Fighter, we'll say Human for now, though I do prefer Halfling for increased mobility when mixed with Step of the Wind. The fighter took a scimitar and short sword, the monk took a handaxe. This way we both get an occasional attack that procs Vex. Standard array of 15/14/13/12/10.
Level 0 - Fighter gets martial weapons and heavy armor, starts with AC 16. Starts with 17 in Str, 14 Con. Monk starts with 16 in Dex/Wis, starts with AC 16, 12 in Con. Fighter takes FS
ef as starting feat, boosting AC to 17; Monk takes Tavern Brawler* for push attacks. Both take Alert for their second feat. Thanks to their higher Con score and HP die, Fighter starts off with 3 more HP than Monk, and get 2 more per level after that. They also recharge more HP during short rests as a result of higher HP die.
* Its a bit annoying that Tavern Brawler is both great and bad for monk. Its great in that monks love unarmed attacks, so anything that boosts it is practically a must-have. Its bad because half the feat does nothing for the monk, so it feels almost like a waste. Honestly, could just as well reduce this to a 5' push on Weapon Mastery and save us all a feat tax.
Level 1 - Fighter takes FS:TWF, gets Second Wind (even MORE HP than monk) and Weapon Masteries for scimitar/short sword. Monk gets Martial Arts, which effectively gives them light, finesse, FS:TWF on Unarmed Attacks, Unarmored Defense, and Weapon Mastery.
Both make an attack with Vex weapon with equal damage, and both can make a second attack of same damage again - everything is very close to the same damage at this point. Fighter gets to keep his Bonus Action open for Second Wind, Monk gets to push someone 5'.
Level 2, monk gets di, fighter gets action surge. Monk uses di to Flurry of Blows for an extra attack over two turns. Fighter uses Action Surge to get two extra attacks on a single turn thanks to Nick. As Fighter's extra attacks include the chance to proc a Vex, the Fighter technically pulls ahead on damage by virtue of increased chance to hit, but its not by a huge amount. Monk does not get
Level 3. Subclass. Monk also gets Deflect Arrows, and how often does that come up in play? No, seriously; I'm used to seeing goblin/bandit and skeleton archers at low levels, and the occasional drow crossbow at higher levels, but is there anything else?
Fighter gets a lackluster level - we get another FS (our third now) and Improved Crit. I'm not sure how the math of combining Vex with Improved Crit will work to actually proc critical hits now, and the damage is kind of lackluster. For our FS, lets take archery so that we can be flexible if we run into a flying monster or enemies on the other side of a gap. More notably, this is about the level we can afford Splint Mail, increasing our AC by 1 again, for a total of 18. Other Fighter subclasses tend to be better at directly increasing damage.
Monk gets three options with different implications. Shadow gives you magic. This is great battlefield control, but costs di and actually prevents the monk from doing damage, though they will get some nice advantage on their attacks next turn. They can even position the darkness in a spot that won't screw over the rest of the party. Using shadow magic actually decreases this monk's overall damage, however, as they want to spend di on the Darkness spell and they don't have enough to Flurry of Blows as often. Might want to swap Masteries as well?
Element... 1 di lasts 10 minutes for a great push/pull option, and has a good chance of lasting until the next short rest option. This leaves us with equal damage to level 2, but excellent control and decent ranged options just from Unarmed Attacks. It also renders both Tavern Brawler and Weapon Masteries obsolete, as we probably want to go full in on Unarmed Attacks with this option.
Open Hand is the only option that really increases damage instead of just offering control. And that's because you actually get to use your new di point on flurry of blows. Topple is the best prone-move in the game, working on any size, of which also tend to have bad Dex saves. This is the only time Monk beats out Champion Fighter in terms of damage, though probably not other Fighter subclasses. Each subclass seems to be giving superior control options to Weapon Masteries, however, instead of more damage.
Level 4 is feat/ASI time. And Slow Fall, but like Deflect Arrow, its questionable how useful that is. Fighter gets to take Charger, or Sentinel, or any other feat that directly increases damage while also boosting Strength. Monk ... needs to go all in on boosting their Dex or Wis. Not only do they need the AC and accuracy, but the lack of martial weapon proficency radically reduces their feat options to Skulker, Speedster, Weapon Training, Resilient, Ritual Caster, Observant, Keen Mind, Defensive Duelist, Actor, Athlete, Lightly Armored and Grappler, none of which directly increase damage like the Fighter's options does.
TLDR: The Fighter has slightly better damage 1-4, even as a Champion, better AC, better Hit Points. This is further exasperated by the presence of any magic weapons or armor, favoring the Fighter. However, the Monk eventually gets far better battlefield control options than the Fighter, putting even Weapon Masteries to shame.
