1050ti 4gb or 1060 3gb

The 1060 3GB is far better. If you need more than 3GB of VRAM, it would still be better than the 1050ti as anything that requires that much VRAM will be too much for the 1050ti to run quickly, where as the 1060 will start using system RAM and still be the faster of the two.

Of course, the ideal card is the 1060 6GB, but I'm sure you've got a budget to work to.
The RAM is a bit of an issue, however there aren't many games that use more then 3GB at 1080p when that's all you have......what I mean by that is, a card with 6GB may see 4GB usage at 1080p, yet the 3GB card will be sitting at 2.8GB usage in the same game at the same settings, the more you have the more it will use. When the card does hit the 3GB limit, which is going to be in high resolution gaming (1440p & 4K), it will slow down as it uses the system RAM, but it won't slow down to the point where a 1050Ti could beat it.