Your looking at about a 25% FPS increase a 6GB variant would be closer to a 40% increase. Is it worth it? That depends on what your happy with considering you can find those cards used for well under $150.
Yes, it's a good upgrade. Something about 30%-40% more performance easily. But you should try at least 6GB model or RX570 4GB. Forget about 3GB model. It have lower memory frequencies and 3GB is not enough for modern games. It will have better performance than 1050TI in very game, but you will have restrictions about graphics settings.
Anyway, you have a CPU that is bottlenecking right now your setup and will bottleneck even more the new GPU. So depending on which games we're talking, you will not have the 30~40% more performance, but way lower than this.
1060 3GB performs better than 1050TI 4GB in every game.
We're not comparing similar GPU here. 1060 is much faster than 1050TI. Much, much faster. VRAM matters, but there's a lot of other things to look at here. So there's a huge lap between them and VRAM would not impact at the point to make 1060 have worse performance than 1050TI.
See this post that I made some time back, regarding this very issue. And, make sure to look at the graphs in the GPU review (for the RX 570, but other cards are, naturally, tested against it) for confirmation. That, by the way, is also with the drivers as they existed in April 2017, so the RX 570 performance has likely improved a little since then.
The 3GB variant of the 1060 is a poor investment, unless it could be purchased very cheaply. The 4GB version of the RX 570 would be better, as it trades blows with the 1060 3GB, except in the aforementioned games where the 3GB cripples the 1060, and, at least in the US, UK, and Germany, is notably less expensive.