I've never shot the Henry, and never will. Life's too short to shoot an ugly gun, and that's one butt-ugly gun.
The Marlin, on the other hand, is a classic design. You can't go wrong with it.
Another good choice is the Winchester model 1892. They've long been out of production by U.S. Repeating Arms (the company that owns the Winchester firearms brand), but a limited production run of 44 mag model 1892s was done in 2003, and you may still find one out there. Browning also made an excellent model 1892 in 44 mag for quite a few years, and you can find like new ones available in the $500 range. Finally, there are some other companies currently importing new Winchester 1892 clones that will be less expensive than a Winchester brand or a Browning, but the quality probably won't be quite up to USRAC or Browning standards.
I'm not as much of a fan of the model 94 Winchester, which is currently produced by USRAC. It's a well built rifle, but the action seems a little clunky to me when compared side by side with a model 92 or a Marlin. It probably has something to do with the fact that the model 94 action was originally designed for a longer cartridge (the 30 WCF or ".30-30"), and modified to handle the shorter pistol caliber rounds like 44 mag.