My favorite non-standard rifle cartridge is my 308 Norma Magnum of course. But as I’ve explained before, that’s because of sentimental reason. It’s not because I think my 308 Norma Mag will do anything the 300 Win Mag I used to have wouldn’t do.
I guess my second place favorite is actually my wife’s Model 94, 32 Winchester Special. There’s some sentimentality involved there too though. I know that in reality, my wife’s 32 Special won’t do anything my own 30-30 Winchester won’t do, but I remember my dad (an “anything 32” guy) claiming, “32s just kill better.” Besides, I think having a 32 Special, instead of a regular old 30-30, makes my wife feel kind of “special.”
My .45-110 (2 7/8" case) Sharps no doubt qualifies as "non-standard" nowadays, but the fact is, it's not my favorite. I like the rifle real well...my wife ordered it for me for our 25th wedding anniversary, but I really don't care to shoot it all that much. It kicks hard, I'm always afraid I'm going to put a ding in it, and black powder is messy. I do love to build ammo for it though, so I guess that's a good thing.