Photoshop CC deletion and erasing is pixelated

I’m having a problem I haven’t encountered before. On my previous laptop I was using PSCC, and it was perfectly fine. But now, whenever I have a selection and delete, or try to erase using the brush, the edges become pixelated.

As an example-

Selection:

Cut to new layer:

What happened, and how can I fix this? I don’t see any cut and paste options for selections anywhere to fiddle with, and changing the eraser to pencil mode isn’t really much of a solution though it does do its one solitary job.