The main reason the Army chose the Trapdoor was the huge surplus of muzzleloading rifle muskets available, which could be cheaply converted to breechloaders. Originally, these were rimfires, before the adoption of the .50-70. Later, of course, the M1873 Trapdoors were made for the .45-70.
One thing about both the Spencer and the Henry, is how long it would take and how difficult it was to reload both. The Henry generally was not issued with any sort of accoutrement to hold loose cartridges. Sometimes a cartridge pouch with the metal inserts removed would do. Although the Spencer did have the Blakeslee loader developed for it, not that many were actually issued, and a pouch was often used to hold loose rounds. Due to the large size of the Spencer rounds, fewer could be held in the same size pouch, and they would still have to be fished out of it and slipped into the buttstock magazine one or two at a time. There was/is one more problem with the Spencer in its rimfire configuration: Should a badly distributed priming compound be contained in the rim of a cartridge, and a magazine explosion occur, the proximity of the explosion to the shooter's face could ruin his whole day! True, the same thing could happen with the Henry, but at least it would "only" ruin the hand or forearm, as has happened with the centerfire versions.
A different factor favoring the Spencer carbine was its handiness on horseback, at least as far as packing it. Of course, both the M1860 rifle version of the Spencer and the Henry could be slung on the rider's back, as was the case when Custer's Wolverines carried them at Gettysburg.
Both are fun to shoot. There is one other potential drawback to shooting the Spencer against our steel plate targets...that is the damage the heavier slug can inflict on the target. In one instance, years ago, I fired at a steel plate suspended by a chain. I was unable to fire more than one shot, as the first bullet took the target off the chain!