If you already have the old PC then upgrade it. If you can only get 4GB RAM on the new system then it's not worth it unless you can upgrade that soon after.
Though I'm confident there is no game in which the i3-7100 would limit the GTX 1050 Ti, making that system (if they both had 8GB system RAM) faster than the i7 + GTX 1050. If you wanted to do more multi-tasking while gaming then that might be a different story.
But why do you have to choose between the i7-3770 + GTX 1050? Wouldn't it be cheaper to buy the GTX 1050 Ti and the i7-3770 rather than buying the new system with the i3-7100?
Even if you had to move down to an i5-3570 get the 1050 Ti instead. Unless you are doing more than just gaming, like streaming and gaming.
GTX 1050 Ti vs GTX 1050 (tested with i3-7100) -
https://www.youtube.com/watch?v=vfZUm-r_sOs