Sometimes, it's just which snare I want to play with that day.
For rock, metal and country I use a 14x7. It's loud and gives me a huge fat backbeat.
For gospel, funk and contemporary jazz. I use a few different snares depending on the vibe I'm feeling for the set. That could be any 10, 12, 13 or even 14 x 3 piccolo snare.
Whatever vibe you are digging is cool. If you doing studio work for someone they may flat out tell you what sound they want so a good selection of snare drums at your disposal is always a good thing.
Same goes for gigs. Some gigs don't require an expensive snare so why bring one.
If it's a low paying gig I bring an inexpensive kit and snare.
I play my 14x6.5 brass for most playing with the following exceptions:
I use a 14x5 maple for lower volume gigs where I want a tight and poppy crack for when we're doing POP songs and some R&B.
I use my 14x5.5 bronze when I need to have my loudest snare because everybody's going to crank it up real loud.
I play my 13x7 maple when I'm going to use my Gretsch bop sizes kit. It looks great with the kit and it's a little higher in pitch but still has a fat sound with the depth. Great for rock where I'm not amplified but I don't have to be as loud as when I play loud rock with the aforementioned loud guitar players.