Mobility - locks lack frequent combat mobility compared to mage. This can be a pain in instances where frequent movement is required, particularly if you a a lock spec (destro, demo) which has mostly hard casts. You are punished for moving big time. Mages with shimmer are not punished for moving and can move frequently. Some specs like fire are able to maintain dps whilst moving during certain windows (FB/hot streak)
Survivability - works differently. Locks have “oh crap” buttons and ways to reverse dmg (drain), mages have ways to avoid damage entirely via ice block, blink and invis. Whilst the lock has arguably greater survivability overall, their primary tool to sustain themselves when injured (drain) comes at the cost of significant dps.
CC - poly is greater in utility than banish. Fear is too risky to see use beyond levelling.
Utility - locks bring combat ress, summons and portal dash. Combat ress is very strong. Summon is good, but nowhere near as good as it used to be pre summoning stones and dungeon teleport. Dash is situational but very good where warranted.
Mages have free food (small, but helpful on occasion), int buff (no min maxer will say no to that extra 3% int you get over scrolls) portals and teleport massively reduce downtime when travelling making mages excellent at farming old content like mogs etc.
I can’t speak for dps atm as I don’t know the exact levels of both classes, but as far as I am aware, mage isn’t a dustbin compared to locks atm. Fire is doing extremely well when it has the traits and gear ideal for it (lucid and blaster master). Arcane is weak yes, frost is still decent for mythic due to the CC. I’m not currently sure where locks sit In the charts, I know destro is decent for mythic due to cleave however. Unsure how locks stand against fire mages when raiding.
Regarding rotations I don’t think one class is simpler than the other. Mages have plenty of spice in their rotation when playing optimally due to shimmer etc. Arcane has a 2 rotation mechanic. Fire has the mastery of the combustion window, frost… Well I don’t know enough about frost honestly. I’m no master on locks but I can’t imagine mage rotations are inherently less interesting than locks as they have plenty going on in terms of keeping on top of your priority list.