I am on a budget and I need to buy a graphics card specifically for DAIN so I am confused whether to buy a card with more cuda cores or one with more vram (what is more important for faster rendering)

Both are important factors. But I would say VRAM is probably more important, as if you don't have enough, you'll be forced to downscale or split frames (which exponentially takes longer!). 12 gigs VRAM should suffice for 1080P. The RTX 3070 is a good option for only 500 compared to the 2080ti 1600, I also believe the tensor cores in RTX cards are used on later versions of CUDnn, therefore drastically improving render times.