I'll throw my two cents worth in here:
I've never owned a Henry. I did handle one at a gunshow a couple weeks ago: seemed solidly made, no obvious flaws in fit or finish, and the lever action was very smooth. Beyond that, I have no comment on them.
I have owned and shot the BL-22, Marlin 39A and Winchester 9422. All very well made rifles that shot very well.
Having said that, the BL-22 is the only .22 rifle of any kind that I have ever owned (and I've owned and shot an awful lot of them through the years) that had an action that failed to lock up and blew a ruptured case back into my face.
I bought my BL-22 very slightly used. This was a few years after the model was first introduced, so it was about 20 years ago now. I took it to testfire at the indoor range. I liked the click-on magtube and the short lever throw was kind of neat. However, I was surprised to feel the lever 'jumping' in my hand every time I fired. After about half a dozen shots, I fired while holding the gun less firmly than before, and the lever jumped all the way open from the recoil when I pulled the trigger, and I got a faceful of tiny brass shrapnel and half-burned powder as the back of the half-extracted cartridge blew up. That was when I realized that the action had not been locking closed, and the only thing keeping the bolt closed during the previous shots had been my hand firmly wrapped around the lever loop.
I took the gun to my local gunsmith, who determined that it had been a factory defect: the angle on the face of the locking wedge was about a millimeter out of true, which was enough with the short throw action to prevent it from locking up properly. (He said that on a traditional long-throw lever action like the 9422 or 39A, this degree of error in the tolerances wouldn't have mattered). He sent away to Browning and they provided the replacement part free of charge and covered the labour.
After that repair, the BL-22 functioned flawlessly and shot very accurately. I was never really comfortable firing the gun after that experience though, and I sold it about a year later.
I've horsetraded hundreds of firearms over the last 30 years, and sometimes gone back to shooting the same model three or four times. But I've never owned another BL-22, and I don't expect I ever will. I just don't feel comfortable with that particular locking mechanism next to my face anymore.