Firstly, there is no .44 "Long" Colt. There is simply the .44Colt. We could argue about the .45"Long" Colt but that's a discussion for another time.
The .44Colt is an authentic chambering for the 1860 cartridge conversions and was the chambering of choice when I bought my Cimarron 1872 Open Top and will be again when I get some 1860 cartridge conversions. Partly because it's authentic and partly just because it's different. Though the originals used an outside lubed, hollow-based, heeled bullet and the current offerings use a standard .429"-.431" .44Mag bullet. As was noted, the 1872 Open Top, which was not a conversion but rather Colt's first purpose-built cartridge gun, was strictly .44 rimfire. However, if you wish to stay compatible with what you already have, there's nothing wrong with the .45Colt. They increased cylinder girth to work with the bigger cartridge but probably not enough to affect handling. If it is even noticeable. If you're into such things, it will be tons of fun to shoot. I'd also recommend Dennis Adler's excellent book "Metallic Cartridge Conversions".