1. Out of the box, I think the Buckmark has a better trigger.
2. The Buckmark's disassembly makes it so you have remove the sights/optics which is not ideal.
3. The Buckmark's I have owned have been very accurate but also liked to be especially clean to be reliable.
4. Ruger Mark IV's are super easy to service.
5. Triggers are Meh.
6. I run a Mark IV 22/45 Tactical suppressed and it has no issues running dirty.
Ruger. I've had the Mark I, Mark III, and Mark IV. They last forever. The Mark I was purchased around 1980. I put thousands of rounds through it. I finally had to replace the recoil spring assembly. Called Ruger and a very nice lady took my order and sent the part to me 3 days later.
The Browning is pretty. The Ruger is accurate and solid.
Browning has a better out of the box trigger across any newer version of the Ruger. If you were in the market for a mark II or III I bet you could find one that outperforms either. However the ease of disassembly of the mark IV is noteworthy.
I currently have a Smith PC victory, Ruger mkiii hunter and 22/45 as well as a Buckmark contour. The Smith is the lightest and the PC mods give it the best ergos. My 22/45 has a bull barrel and an old school tube style red dot. It's bulky but also a mag dumping delight on the steel. The Buckmark contour is accurate and the weight is present but pleasant.
My 22 pistol journey started with a rohm rg14 and a Jennings j22 around 1990. Everything was an improvement from there but my first Buckmark camper was a great gun as well as my first mark ii. I also had a 22/45 hunter I let go of as well as a pencil barrel mark III. My Beretta neo was a flash in the pan for me that I gave up on within a few months.
You really can't go wrong with either and both will have great mods by tandemcross. I highly recommend their magazine bumpers for either and flat triggers. Their captured spring or gearbox for the Buckmark will drop about a half pound or more of pull weight too. With either model you don't loose much accuracy with the lightweights and have a versatile plinker for shooters of all skill levels.