At 1080p, most games released so far still don't even use all the vram of a 6GB card. You would really only be hitting vram limits on an 8GB card when using ultra textures and using ray tracing, though neither card can run ray tracing at high enough fps to bother using.
As for the other graphics settings, even with 8GB vram, ultra textures will likely work fine at 1080p. High graphics settings may be a challenge to run on newer games at 60+fps and could require the use of FSR 1.0/2.0 for either card or DLSS if you get the RTX 3060. Regardless of what you pick, FSR and DLSS are not the best looking at 1080p, but DLSS is definitely has the better image quality at lower resolutions.
Currently DLSS is still better quality than FSR 1.0 and the newly released 2.0, which will take awhile to get into more games. DLSS 3.0 is going to be coming sometime this year and will or should bring even more improvements over current DLSS 2.x versions.
If it's not too far off in pricing, I'd personally keep saving and try to get a 3060 TI and have the better all round performing card, since it's faster than the 6650XT and as fast as or close to a 6700 XT or 6750XT. You can also run 60+fps ray tracing at 1080p with DLSS or FSR with the 3060 TI.
You might also eventually have the option of a cheaper 6700 non XT that just recently released. If you're not interested in ray tracing or DLSS/FSR and just want the faster card of the two you mentioned, get the 6650XT.