Off the top of my head I don't think the higher memory will help Dolphin, but if you ever end up playing any games on it the 6GB will definitely help at higher resolutions
Thanks for the replies. The truth is I'm not really into PC games, at least not the kind that push GPUs to the limit. We have a Wii, a Wii U, and a PS3. We play games on all of them, but mostly Wii U lately.
Playing Wii games in high definition using Dolphin is the main goal. If more GPU memory or more Cuda cores will help Dolphin, I'll go for the more expensive card. But that's a slippery slope too. The 1070 or 1080 cards are faster still... but I can't justify spending $500 or more on a graphics card. So it will be either the 3GB 1060 or the 6GB 1060.
Thanks!
the 3 GB version is fine.
The 3GB should be plenty.
Edit: ninja'd