Slow Video Render? incl. New & Old PC Specs
Rendering in 1080p takes up more resources than 720p, so it is normal that your render is slower than usual, even though your new hardware is superior. 1280x720 = 921600 pixels per frame, 1920x1080 = 2073600 pixels per frame. The software has to render 2.25x the amount of pixels per frame, so you can expect it to take about twice as long.

the 770 GTX has 1536 CUDA Cores, the 260 GTX has 192, so your new graphics card is far superior for video rendering. In theory it should be a lot faster for video rendering.

Depending on your version of Sony Vegas, you can enable CUDA for your Nvidia graphics card, this should increase the speed. Go to Options >> Preferences... and go to the video tab. In version 12.0 there's a dropdown menu labeled "GPU acceleration of video processing". Set the value of the dropdown value from "Off" to your Graphics Card ("NVIDIA Corporation (GeForce GTX 770)")

If you're not using 12.0, it comes down to selecting the right render settings in the Render As... menu. Since you're uploading to YouTube, I recommend rendering as Sony AVC (.m2ts) and selecting the template 'Internet 1920x1080-30p'. The ratio rendering time to video length should be about 1:1. Still, Sony Vegas 12 had a lot of updates regarding GPU acceleration and rendering in general, so consider upgrading.