Except the actual successor to the 1060 cards would be the 1660 models, not the 2060, making the gains for the last generation smaller. It only really makes sense to compare performance based on what's available at similar price points, not arbitrary model numbers. The GTX 970 was a $330 card, and the 1070 was a $380 card, so the $350 2060 and the $330 3060 are more successors to those. They don't keep the price points exactly the same between generations though, so to get meaningful results one would need to calculate the change in performance-per-dollar, not just performance.
Nvidia hasn't yet released a successor to the 960/1060/1660 this generation, something roughly around that $200-$250 price range with a TDP around 120 watts. It's also likely that the shift in model numbers that the higher-end cards saw last generation will work its way down the stack in place of something like the "16-series" they used before. So that card may be marketed as an RTX 3050 or 3050 Ti, despite not bearing much resemblance to the sub-$200, sub-100 watt cards Nvidia has traditionally associated with the "x50" model number. If I had to guess, a "3050 Ti" would probably perform a lot like a 2060, with 6GB of VRAM and an MSRP around $250-$280. Probably closer to the lower end of that price range considering there were already some $300 2060s last year, though it's hard to say in the current market, and I wouldn't expect the cards to be available for anywhere close to those prices for at least a number of months.
If there's a 3050 Ti, then there may also be a 3050 priced closer to $200, with performance more like that of the 1660 SUPER, only now with RTX functionality. I'm not sure how usable something like that would be for enabling raytraced lighting effects in games though, since the 2060 is already barely usable for that purpose.