I have the exact opposite opinion. I prefer 360 to XB1 because the sticks are tighter.
This must be something entirely subjective and vary by person, but, I find tighter sticks make it easier to make fine adjustments, not harder. For me, on a loose stick, the tiniest increment that I can have my thumb move the stick is larger than the increments of precision I need in the game. It's too easy to "overaim". Like imagine a super-sensitive mouse that moves the mouse all the way across the screen by moving it only half an inch. It's too sensitive. Your hand can't move it slowly enough.
Put another way, imagine driving in real life and having to make super-precise turns. The wheel has no tension and is entirely loose, loose as a pinwheel on a stick toy that spins in the wind. Yeah, I guess you could get the wheel to the correct spot faster because there's no resistance. But COULD you with any precision? I think that would be insanely difficult without any tension or feedback. To me, that's a loose stick. YUCK.
BTW, my favorite stick of all time is N64. Take from that what you will...