I play MNK main and only started trying out SMN recently.

I can talk about MNKs easily. I really like their playstyle. Though movement may seem like a hinderance from the outside, I think it's a lot of fun. It's a third dimensional sort of combat. There's a lot of rhythm to it as well since the gameplay lends itself to muscle memory.
Not to mention the damage is pretty amazing (top), but I'd be playing it even if it wasn't.

SMN feels like the caster equivalent to MNK. I've played BLM a lot but I'm only now trying SMN out. SMN is like MNK in that it has ramp up and it's really about sustained single target.
However, SMN has much better options for AoE than MNK. Not to mention being ranged feels a lot safer if you want to keep up dps.
I doubt SMN dps can beat MNK dps.
Particularly because fights that are bad to SMNs are bad to MNKs, and fights that are good to SMN are good to MNKs.
The notable exception is, again, aoe. SMNs are great at cleave and manage any overall aoe better than a MNK.

SMN utility -
Eye for an Eye (amazing for everybody who gets it, shorter cd for SMN/SCH)
Virus (nerfed the uptime, but still a great ability. SMN reduces int/mind(?) as well)
Instant Res (of course, you shouldn't want to use this but things happen. SMNs can save healers mana and concentration)
5% slow Shadow Flare (Not sure the extent this works on bosses, but it's pretty great. It seems to have no diminishing returns as it's permanent once the mob stays in.)

MNK utility -
Mantra (cross class version sucks, 20% healing increased can be great)
-10% INT on Enemy via Dragon Kick (permanent debuff since you keep it up for your rotation).
Silence (we have one, but you should never really ask the MNK to do it unless it's really no other choice. Huge TP drain, very clunky to use. Though I have done ADS with it.)

The SMN utility seems like more but the Dragon Kick debuff being fairly permanent can't be underestimated.
Of course, it stacks with virus and eye for an eye. There's also nuances like chaining Eye for an Eye if your other party members have it.