Even "souped up", the .45 Colt is still a pistol cartridge, as is the .44 Magnum. Both are underpowered compared to even medium power rifle cartridges like the .30-30.
This is not necessarily true. The 44 Mag compares reasonable close to a 30/30 at 100 yards. Elmer Keith took Deer at 600 yards with a 4" 44 Mag and the slugs were passing through the Deer. The article is online if you wish to google it.
The thing about big bore revolver rounds is the typically heavier weight bullets than your rifle cartridges have in them. This makes them great penetrators and helps to level the playing field somewhat, and make them an ok choice for Deer.