Two fine choises, but what are the criteria besides being a .22 LR?
For a plinker, the Buckmark is a much better deal. From what I was told, there is no difference in trigger quality in models, so the lower cost camper model is a great deal.
If you want to get a model for competition, a Sig is probably a better choise. The Buckmark has competition models, but I get the feeling that the high end for Sig is higher than Brownings.
My Buckmark needed a couple hundred rounds to wear in properly. The only ammo problem I have now is with very hard primers. I had one Remington take 6 attempts before it went off. Now each trigger pull left a deep dent on the casing, so it was not the Buckmark. I got a deal for a Buckmark Plus Micro, which means that it has nice walnut grips (the plus part), a 4.5" barrel, and costs more (again, the plus part).
The trigger pull is light and crisp. The only better trigger I have felt is for a S&W 625 from the Performance Center. I guess I got lucky on that part, but I did try it out before buying. After shooting my Buckmark I can really acutely feel the flaws in my other triggers.
I found that getting a fiber optic front sight did wonders for my grouping. Black on black sights never work for me.
I doubt I will ever be as accurate as the Buckmark. This more .22 LR as I can ever use.
Really, if you have the money either way, you will not go wrong.