As far as I'm concerned, sound transmission from current professional wireless especially the Line 6 Relay series is indistinguishable from cable. And I like all the things that people have mentioned that you can do if you're wireless, but the main reason I use wireless is because regardless of whether I was moving on a bigger stage or relatively motionless on a smaller one, I would ALWAYS end up stepping on my cable and jerking my bass several times a gig. Now I am so used to wireless I always use it, even at rehearsal. I don't necessarily move a lot, but if I do want to change location, I go where I want with no problem, no tripping, no tangles.
The downsides of wireless are batteries and securing the transmitter. I use rechargeable batteries and put a new set in before every gig. My Line 6 Relay G50 can easily go 5 - 6 hours on one set. Also if you don't secure your transmitter and it falls yanking on the instrument cable, you can easily screw up your mini-xlr connector on some wireless units and you'll have to repair or replace the cable. I finally found a little pouch that I can attach to my strap that fixed that problem. Setting up wireless at a gig is really simple too, especially if you already have a pedalboard to put your receiver on or use a rackmount unit.
If cable works for you cool, because good wireless costs a few bucks. But other than the expense, it can offer some nice advantages for relatively little hassle.