GPU accelerated encoders like NVENC, AMFA (or whatever the AMD variant is called) and Quicksync have these pros/cons:
+ fast
+ very little performance loss
- inefficient (quality per bitrate is bad)
CPU based x264 encoding has these pros/cons:
+ efficient (good quality per bitrate @very fast preset and slower settings)
- high CPU load
Pascal Cards seem to deliver a better NVENC encoding efficiency that older cards, but x264 is still king, when it comes to low bitrates (<10.000kbit/s).
For local recordings, where you are not restricted to a low and constant bitrate, I would use Nvenc with constant rate factor aka CBR set at 19.
For streaming use x264 very fast. Games like Destiny 2 can only use up to 4 real cores, so with your CPU there are some cores left for streaming without reducing game performance. You can try x264 preset "fast" or even "medium" as long as you don't stream with 1080p 60fps (which would be the worst setting for streaming anyway).