Possibly an unanswerable question but I've got to ask :-)
The spec for both is roughly the same - i3 7100U, 4GB and 128GB SSD, and I will probably swap out the RAM and SSD for something larger, but can't make my mind up which is best.
The 510s is £380 and the positives for me are the backlit keyboard and the screen surround matches the rest of the laptop rather than the usual black.
The 320s is only £330 and doesn't have a backlit keyboard and the screen surround is black, but it's £50 cheaper and has a free M.2 slot inside, so I could have an SSD and a HDD, should I wish.
Small issues i grant you but it's filling me with indecision. Appreciate it if anyone has strong opinions either way, or knows something I don't - very possible!