Sorry, was out this weekend.
First, yes, mame always applies its maps to all gamepad type joysticks, but if the u360 is mapped to digital, then only 9 of the 81 squares matter. (the corners, center edges, and center)
The most common issue people run into is probably with qbert, as mame applies a normal 4-way map by default, and if you map diagonal-only on the u360, mame tries to convert them to cardinal-only with sticky rules, but without a prior cardinal direction to stick to (it's diag-only), mame has problems.
As to what's better, u360 is better, but AFA inside mame goes, mame's is almost as good.
u360 map
pros:
can move cutoff points aka resize cells (need to hand edit cfg file though)
can remap for all emus and games, not just mame
possible to map each joystick differently
can set different maps for each game (with FE, script, & third party app)
has GUI remapping app
cons:
needs separate app to automatically change maps (and a FE that can run it)
can't auto-change if using mameUI or plain mame without a FE
may need to set a mame map anyway in some cases (like sometimes qbert)
mame map
pros:
works with all analog joysticks, not just u360
no need for an external app to remap
mame automatically remaps for 8-way & 4-way, defaults are okay for most people
can set different maps for each game (with gamename.ini files)
there is a third party GUI remapping app
cons:
cannot change cell size
only one map can be set to all joysticks at a time
only works on mame
can be confusing to remap by hand (but there is a GUI app to do it for you)
FWIW, the best way to "fix" mame so it doesn't mess up u360's maps is a generic 8 way map "-joystick_map 7778." for all mame games, and let u360 (& FE/script/app) handle the remapping.
Me, I use mame's maps because I never setup the script/app stuff, and am happy with mame's for now.