My vote goes towards the original Xbox. It did a lot IMO and doesn't get any recognition. PSP will be my second choice.

GaneCube. Derided for looking like a lunch box, yet such a capable enjoyable machine with many original games.

Those are both significant, important systems. But, I don't see that they get a lack of recognition. I think pretty much everyone recognizes their significance.

Can we ban the Dreamcast from this discussion? There's already a religion dedicated to that.

I'd go with OG-Xbox as well. I grew up with that system and it had several underrated gems, a personal favourite being Jet Set Radio Future.

I think it's SEGA Saturn, it had some awesome gems like Panzer Dragoon Saga and Burning Rangers.

There are only three correct answers here...

OG XBox did a lot but gets little recognition.

VITA was a great handheld with a lot of great games especially Japanese games. The problem here was no 1st party support from Sony.

The WiiU was a decent home console with great games, but was underpowered for what it was, mismarketed, and lacked proper 3rd party support.

Every other console gets recognition regardless of performance or flat out sucks, so I do not see the point in picking them. With that in mind, I vote OG XBox as it had far less mistakes than the other two did. It simply just went through the pressure of being the new kid on the block and people did not jump on it as much as they could have.

EDIT

Sega Saturn also deserves credit, but fell victim to possibly the WORST launch strategy in gaming history.  My vote still goes to OG XBox.

Original Xbox and Gamecube would be my two picks.

edit: 6th gen in general was easily the best era of games, IMO. All three consoles were worth getting and had a great library of games, especially the PS2.

80+ million sold is underrated? oukay

Gamecube and N64

Gamecube and N64.
Made some of the most iconic games of their generation and pushed gaming a lot, but really didn't dominate their gen sale wise which is a shame.