I am a huge fan of the Marlin 39. The older 39A is as good of a shooter as you will find bar none. The Henry is a decent rifle too but just not what that older 39A is. Get the Marlin and if you don't agree, I will buy it from you for the price of a new Henry.
Think about the resale value the day after purchase. Think about the resale value 5 years after the purchase. Which rifle will tend to retain its value and/or appreciate?
Either rifle will meet your requirements for accuracy. I think chip monks are kind of cute but to each his own.
I really like my Marlin 39AS that I bought new in the mid 1990's for about $300. It has a nice walnut stock and cut checkering, a 24" barrel, deep bluing and an excellent wood to metal fit. The added safety is not a problem. With Wolf match Target ammo, it shoots one hole groups at 50 yards. It has a wonderful full size feel and heft like my 1968 .35 Remington Marlin 336 RC.
I would go with the Marlin too, but I have never shot a Henry, I am sure they are fine rifles too
The first rifle I ever bought was a 39A,paid $79 for it new still have it but my bros beat the piss out of it when I was gone in the USAF, but it might be ugly but still is accurate,
I also have a 39 Century LTD it was the centennial model that the same bros shot while I was in the USAF, I had kept it hid from them as I wanted to keep it unfired but so much for that, but at least they didn't tear it up too bad
The older Marlins are classics and set the standard for lever action 22s. There's a very good reason that the same basic design was produced for over a century. The Mountie (carbine) version draws a premium.
My Marlin 39A was made in 1950 and left to me several years when an uncle passed away and no one else wanted it. It has the old Ballard rifling rather than the newer Micro Groove rifling. The deeper cut Ballard rifling took much longer to produce and results in very good accuracy using lead bullets. Most .22 rounds I shoot are lead and not jacketed. I was told by a couple Marlin shooters recently that the value of mine is somewhere around $650, but I have no intention of selling.