Lots of good points for both. I'm a big LA fan and a certifiable .22 Junkie, so I'll give you what I consider to be some of the high points of both.
Marlin: I've had my 39M for about 25 years now. It's had more rounds put through it than I could estimate with any degree of accuracy. Nothing has ever broken nor worn out. It's action has become slick as glass with use, but still locks up as tightly as new. It will cyle and fire reliably with just about any .22 RF ammo you're likely to run across. CB caps, shorts, longs, LRs, Colibris, shot cartridges - you name it. In these days when shorts can be hard to find and are more expensive than LRs that may not matter to you much. Personally, I like the option. SV shorts are nearly as quiet as Colibris and hit much harder. IMO, more humane on larger garden pests, especially if your placement isn't quite perfect. At about 6 1/4# with sling, it isn't a featherweight, but its great balance makes the little bit of extra heft translate into smooth tracking on moving game. Drilled and tapped for receiver sights and scope base. Weaver-style bases available so you don't have to stick to tip-off rings. Take-down receiver makes cleaning the barrel from the breech easy, and you don't have to disassemble the action to get to everything.
Browning: I've had mine for several years, but it hasn't seen anywhere near as much use. Mostly because I'd have to add a receiver sight and sling swivels to get it on-par with the Marlin as far as my personal preferences go. Very trim and handy. About 5 1/2#. Slick action with an unusually short throw and decent trigger action. Grooved receiver. Not drilled and tapped for receiver sight. Stock flip-up leaf is fussy to adjust. Epoxy stock finish is a bit gaudy for my tastes, but very tough and the wood on most seems to be pretty nice. Nice straight grain and mellow color. Muzzle has a recessed crown. Keeping the action clean is more of a chore, as you have to pretty much disassemble it to do a good job. No provision for sling/carry strap, but Uncle Mike's can fix you up.
Both will shoot better than I can with their favorite ammo. Both will outlast me by a few decades with a little care. Both make a great little do-it-all utility rimfire. IIWY, I'd go check out both and see which one suits your fancy best. IYWM, you'd get both