I am by no means a Premier fan (never tried it) but I've found Media Encoder to work supremely faster and produce flawless results (this was a tip I learned from our post/finishing house). Exporing straight from Avid is actually faster and produces better quality when exporting 1080p h264 files. I always have to re-export/encode through another software. the encoding times move at a glacial pace and the image quality has not once been even remotely acceptable (my experiences have been with either 1080p or UHD footage). Whether I export my timeline straight from Avid as a ref or it's an external MOV, image sequence, etc.

Their customer service is terrible - I gave them my system specs and they said Squeeze would be able to encode any footage quickly, beautifully and easily - especially with 40 cores. They also don't support mxf transcoding to DNxHR (huge problem for an editor whose client wants UHD dailies). They initially advertised their new GPU acceleration which, upon download, I learned is no longer supported. I'm on Squeeze 11 Pro and it is an ABSOLUTE NIGHTMARE.

Handbrake vs adobe media encoder