I think you might have got the 6700 XT and 7600 XT backwards in your post (or their VRAM amounts). The 6700 XT should be 12 GB VRAM, the 7600 XT has 16 GB. Although both should be cheaper than the 6750 XT, but I suppose that will depend on your market.

Anyway, if you're considering up to 480 euros for the 4060 Ti 16GB, check the prices of the RX 6800 (non-XT) or RX 7700 XT. In the US at least, they're usually a bit cheaper than, or about the same price as, the 4060 Ti 16 GB and depending on your sources are usually at least equal in performance. Another thing to keep in mind is that the 4060 Ti 8 GB performs almost exactly the same as the 16 GB version, in gaming at least, and the extra VRAM isn't likely to be all that helpful at 1080p, and at a price closer to the 6800/7700XT.

Of the 3 cards you listed that are 400 euros +/- 20, the 6750 XT is going to be the winner, especially if your post is accurate and it would cost you more money to get the slightly weaker 6700 XT.

If you're really trying to stay way under 400 with the 3060 or 4060, get the 4060. It has enough performance advantage over the 3060 to justify the price difference you've listed. As a bonus, it's extremely power efficient, especially compared to most of the AMD options being discussed here. Something to keep in mind depending on your electricity costs and your current power supply.

Here's some more reading material for your own research:

Tom's Hardware GPU hierarchy https://www.tomshardware.com/reviews/gpu-hierarchy,4388.html

Techpowerup has relative performance ratings which you can gauge against relative prices to see if upgrading from one card to another is worth the money https://www.techpowerup.com/gpu-specs/

GamersNexus write up on best cards by budget category (based on US prices but the tiering still seems close to what you've laid out) https://gamersnexus.net/gpus/best-worst-gpus-2023-gaming-100-2000-video-cards

UL (owners of 3DMark) sorting of GPUs by value (not sure how well it'll reflect prices in your market) https://benchmarks.ul.com/compare/best-gpus?amount=0&sortBy=VALUE_FOR_MONEY&reverseOrder=true&types=MOBILE,DESKTOP&minRating=0

Do you want to game on Linux? If so, I'd recommend you to scratch those Nvidia GPUs off the list.

I know you said you don't want to buy second hand, but if I were you I'd buy a 6800 xt second hand. That's by far the best bang per buck you'll get. I've been buying second hand gpu's for over 10 years and have never had any trouble. Just don't buy any dirty, overclocked or used for mining cards and you should be fine. I already looked on OLX and there are a few between €350 and €400. If you really want to buy new I'd go for the 7600 xt.

Good luck!

You will almost certainly want something with more than 12 GB for the future.

The RX6000s offer a lot of bang for the buck since AMD released their fluid motion frame generation. I've been using a 6600 (non-XT) at 1440p and it does surprisingly well. You sure about those prices/specs though? 6750XT for less than 6700XT? And a 6700XT with 16GB?