When I render low-resolution videos (from After Effects), images that have been upscaled look horribly pixellated. Here is a sample:
This issue has been raised in the past in this thread, with no solution given:
Pixelation in small h.264 exports
A related problem is that whenever I change the output resolution to anything under 1080p, the estimated file size does not go down, even though the resulting file actually is a lot smaller. This seems like a bug to me. It's as though Media Encoder just isn't correctly handling anything below 1080p.
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Well, at the risk of sounding obvious, 960x540 uses 1/4 the number of pixels as 1920x1080 so indeed, the image will definitely be less sharp. 
Your image looks fairly normal to me. One thing you can try however, is to turn on the bicubic scaler for that particular layer in After Effects before sending to AME.
Simply changing the resolution will not affect the estimated file size. It's the bitrate that affects file size. If you dont change the target bit rate, it will report the same estimated fil
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Well, at the risk of sounding obvious, 960x540 uses 1/4 the number of pixels as 1920x1080 so indeed, the image will definitely be less sharp. 
Your image looks fairly normal to me. One thing you can try however, is to turn on the bicubic scaler for that particular layer in After Effects before sending to AME.
Simply changing the resolution will not affect the estimated file size. It's the bitrate that affects file size. If you dont change the target bit rate, it will report the same estimated file size, but you may still get a smaller file in the actual export. Here's an article I wrote that talks about this a bit more:
Bits and Bytes: The Simple Math of Premiere Pro’s Exports — Video Review & Approval
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