I'm not sure about Photoshop Elements as I only have Photoshop, however I've just used Photoshop to resize your car pic and these were the settings I used to get more-or-less the same image quality/file size.
---------------------------------------
Adobe Photoshop CS4
Size: 1333 X 1000
Resample: Bicubic Sharper
Quality: 65
Embed Metadata already off in 'Save For Web'
File Size: 334KB (342,786 bytes)
Pic (Direct Image Link):
---------------------------------------
For the record I also tried Affinity Photo Bilinear with a quality setting of 88 (which made a 352KB file), but it's noticeably softer than the above two, so I'm not entirely sure why that's the default Affinity resampling method rather than say Bicubic or Lanczos 3 Separable.
Also, although it shouldn't affect your smaller photos, it may be worth going to Edit > Preferences > Performance, and changing the View Quality setting from 'Nearest Neighbour' to 'Bilinear (Best Quality)'. It's set to 'Nearest Neighbour' by default, which displays jaggy edges in Affinity Photo when a larger image is displayed smaller than 100% (it doesn't affect the export quality, only viewing in Affinity).
Hi tbonecopper,
Don't resize the document (pixel layers) while you are working on it (using the box control handles). Resize it only when you are exporting, entering the dimensions you want in the Export dialog to prevent resampling the image twice. To reduce the JPG file size further you can also click on the More button in the Export dialog and uncheck Embed metadata.
