Will the GTX 1060 6GB be as powerful as my old GTX-670-SLI or would the 3GB model be just as good since I only game at 1920x1080,or would the AMD R9-380 4GB be a better solution. I don't care about having the fastest no more ,just the best bang for the dollar and play the newest games.
3GB vram isnt enough this days even at 1080p. I have 3GB card so trust me so i would recommend you avoid it. 1060 6GB ver will be much better choice or you can go with RX470/RX480 4GB/8GB.
I do not suggest to you 3gb vram in these days. You should buy 6gb 1060. 2x GTX 670 means = GTX 970 (might be %10-15 lower performance than your 2x 670). Actually, you might not notice FPS difference in screen but if you have 2gb 670s you'll notice 6gb vram + more powerful single GPU performance scale, smoothness in every game.