It's really not a fair comparison. The appeal of the NES Mini is in the nostalgia and novelty factor. If we're just going by the games, I'd personally say Rare Replay since I already own most of the NES games in some fashion. Yet I still want the NES more.

The NES Mini has great games up and down the list, but it is obviously limited to NES games. Depending on your tastes, they haven't all aged that well.

The Rare Replay spans generations, and has some pretty new games. The biggest problem is it is missing some of their best games. No DKC trilogy and no GoldenEye is a big part of the Rare library to be missing. That leaves me with only a handful of games I actually care about in the list:

Blast Corps
Banjo-Kazooie
Jet Force Gemini
Perfect Dark
Banjo-Tooie
Conker's Bad Fur Day

How do these 6 stack up against the 25 or so NES games I would like to play? Well, Perfect Dark is one of my favorite games of all time. And I would probably actually get more play time out of these 6 more modern games...

I went with the I can't choose option.

NES Mini easily, because forget hardware also, while you have to buy or to have XB1 for Rare Replay.