Is youtube 1080p full hd better quality than high quality 1080p hd when using adobe premiere pro?

High Quality 1080p HD is one pass variable bit rate with a target bit rate of 20 Mbps using Hardware encoding if available.

YouTube 1080p Full HD is one pass variable bit rate with a target bit rate of 16 Mbps using Hardware encoding if available. 

Image quality should be about the same; however, the file created via YouTube 1080p Full HD should be about 80% smaller resulting in a faster upload.

You can queue both at the same time in Adobe Media Encoder by using the Add Output button, compare the results, and upload whichever one you prefer.

Both options you mentioned give you the same resolution (1080p) so doesn;t matter.

As for frame rate, this depends on the frame rate of your sequence.