Henry H001 is what I have. It's a very nice .22 lever and is a lot of fun to shoot. In fact, it grows on you the more you shoot it. Accurate and the action is extremely smooth and lightning fast. I will be keeping this one.
It is a pricey rifle for what you are getting, in my opinion. The stock set is nice walnut, but the receiver cover is alloy with a black coating like enamel. I don't care for that, and it actually gives the rifle a sort of toylike appearance. Also, the barrel band is plastic. I know there are replacement metal bands, but as far as I am concerned, it enhances the toyish look of the Henry.
I've never handled or even seen the Mossberg, so I can't comment on that one.