I’ve never owned any of these, but here are my impressions based on the guitars that I’ve tried and what I like:
Bourgeois: I’ll be honest, every Bourgeois I’ve played was a good, or even a great guitar. I was particularly impressed by an Aged Tone mahogany Bourgeois that was probably the most “cutting” guitar I’ve played. I wouldn’t want that kind of sound in my main guitar all the time, however, and besides that one most Bourgeois haven’t jumped out to me as a particularly impressive-sounding guitar. I do think the Banjo Killers are very cool guitars, if only because of Bryan.
Collings: I think they are the most consistent of these brands. Every Collings I’ve played felt and sounded great, and remarkably consistent. From the first time I played one, I thought they were awesome, but I don’t think I would like to own one as my main guitar. I just can’t see myself spending that much on a guitar that has thousands of others that look and sound extremely close to it. I do love the vibe of Jake Workman’s satin D2HAT and Julian Lage’s OM.
Martin: Probably my favorite of these brands, if only for “cool factor” (as @Mason_Crone describes it). Lots of my favorite artists played Martins (including, but not limited to: Tony Rice, Bryan Sutton, Kenny Smith, Julian Lage, Joshua Lee Turner, Eric Johnson, Dan Fogelberg, Jim Croce, Joni Mitchell, Stephen Stills, and many more guitarists from the folk era). Of course, if prewar Martins count, then they are definitely the best guitars I’ve ever heard/played. I can’t say Martins are overall the most consistent guitars, and I have played some old and new Martins that I wasn’t impressed with. However, I most of all like guitars with character, and I think a lot of Martins are just that (even the ones that aren’t the $150,000 kind). As Kenny Smith puts it, it’s like finding “your sound”. I’d love to play on some '50s Martins sometime soon.