I don't have a lot of experience with imgix, but http://filepicker.io will resize your images on demand server side, and its all hosted in your S3 bucket/pretty reasonable pricing.

Example:

640x400 and formatted as a jpg

https://www.filepicker.io/api/file/rHA62UiiQyCZdEyw6rgw/conv...

200x200 and a png

https://www.filepicker.io/api/file/rHA62UiiQyCZdEyw6rgw/conv...