On average you'll probably have a significant CPU bottleneck if you went with the 1660Ti, but it all comes down to what games you'll be playing and at what resolution. Some games will be more CPU intensive and you'll really see the old 3770 hurting performance, other games will be more GPU intensive and the 1660 will be free to give all it has. With the 1660Ti you will run into games that are normally GPU intensive but the GPU will be running fast enough that the CPU can't feed it anymore, and you won't see any difference between the 1660 and 1660Ti on CPU intensive games as the CPU will still be holding things back.
If there is one constant in the universe it is that AAA games eat resources. Whether it is something like Crysis that pushes graphics cards to the limit through poor optimization or Assassin's Creed which melts CPUs with DRM, you'll always run into games that are difficult to run... and the 3770 isn't getting any faster. As a result, I'm not sure that a 5 year upgrade cycle with an already old CPU and a mid range card is a reasonable thing. I understand the lack of money, but CPUs have a 5 year span on expected viability, and graphics cards even less, with the expectation being about 3 years on a midrange card for AAA titles.
If it were just speed there wouldn't be a problem. 6 year old hardware could hang with modern games without issue if it was computational speed alone. There are also additional technological advancements that happen to improve performance, and older hardware will take a big performance hit simply because the old stuff doesn't support it. I'm not sure a 3770 will stand the test of time much longer, especially since AAA games are getting to the point where they recommend 6th gen Intel CPUs (heck, VR games already require a 4th gen CPU). It won't be long until they are requiring them. I'd say the 3770 has about 2 years of new release AAA gaming left in it.
The 1660 though should be good for 4-5 years. Right now it is a good investment. You'll have a few good years as a mid-range card before things move on and you have something more akin to a current GTX 1050 or 750 Ti. Both of those are still good cards and play just about any game you throw at them, but they are decidedly lower end and require you to play at reduced settings.
I would suggest in about 2 years time looking for a CPU, motherboard, and RAM upgrade. I just don't think you are going to get 5 more years out of an i7 3770 if you want to keep playing new games. Plus, it is easier to justify getting the 1660Ti if you are planning an upgrade because you'll see more of an upgrade once you get your new hardware as the current hardware would be holding the 1660Ti back.