The 1050Ti is relatively a similar card than your 650 Ti, meaning there's a couple of more powerful, more expensive cards in the series. However, there's a lot of new technology involved, so the energy efficiency has improved as well as the overall performance. It should run AH3 very well on a single 1080p/60 Hz screen with quite a lot of eye candy.
It should also fit your system even better than the current card since the rest of your system dates closer to the new card than the old one. The new 10## cards have been successfully installed to much older systems.
If you're hesitant, the GTX 1060 3 GB might not be too much more expensive, depending on brand. Either way, based on benchmarks and comments here the performance boost will be highly noticeable.
