I have both a Winchester and a Browning in .22 lever guns. The Winchester is by far the better of the 2. I love the fit and finish of the Browning, as well as the Browning's ability to feed any ammo. The Winchester is just a better shooter though.
Strange as it may sound, I like the longer throw of the Winchester over the short throw of the Browning. One of the reasons I like lever guns is the act of levering them, and the Winchester gives a little more of that.
Both have had to make trips back to the factory. The Winchester for feed problems, and the Browning for trigger work. Both companies were compareable in the treatment I recieved.
Neither are as accurate as my ancient Marlin/Glenfield model 60, or my scoped Ruger Mark II, but I went lever action because I like it, not to win any matches. This isn't a slam against the lever guns, as they are not the best choice for top accuracy. That being said, there isn't really that much difference between dime sized holes and nickle sized holes.
I give the edge to the Winchester for returning more bang for the buck, decent customer service and better out of the box feel. The Browning may be just a tad too pretty. It says I like being the center of attention with my deep blue and gold trigger, and just the right combination of straight and curved lines. The Winchester says "let's go shoot". Lots like a burger and fries as opposed to a steak dinner.
Browning, Winchester and Marlin are all comparable with classic lines and general high quality. I believe Ruger also makes a lever action in .22, but I just don't care for the looks of it. Like all Rugers though, it should run like a "truck", meaning indestructible. I have no experience with the Henry line, but from what I've heard, they aren't the best choice.
Let us know what you end up with. Since you already have a 10/22, it sounds like this is to be a "fun gun, take along on a hike in the woods, go to the range and have a blast" type. Lever actions were made for that