Yes there's a difference. Ask any owner of a gtx970 with its 3Gb of regular high speed ram and the 0.5Gb of lame duck ram. For low end games, think B to A type games, online stuff like the Sims etc, then a 3Gb is fine, there's not much demand on the ram. Some AAA games are different, especially at higher resolutions and can put a huge demand on the ram, which is why 6Gb is about minimum standards for the top line cards. But it's a gtx1060, so higher resolutions are pretty much off the table, but still can get hefty ram usage. If you are playing AAA type games, then better to have the ram and not use it much than not have the ram and suffer when it is needed.
Brands? Pretty much alike. There's enthusiast class cards those are the more expensive ones, that are made for harder core gamers who like to get every erg of performance per dollar, and will usually push the OC, and there's regular cards, mostly based on the FE, with a paint job. But both are still 1060's and perform at that range. Brands are most notably a personal preference, both classes of gpus will perform similarly.