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!
I would hang on for a while. Spectre issues need to be addressed and are being so slowly.
An i3 Intel 7th gen CPU not as good as a 6th gen i5 and the i5 will be a tad more expensive.
Microsoft just published an update for skylake 6th gen, and others, against Spectre. It's a microcode update from the windows update catalogue.
As Windows 10 changes every six months or so, next one early April at a guess, then it gets a tad more heavy on the CPU.
As you're going for a laptop don't curtail your choice to a certain manufacturer but look around. I would certainly recommend Intel over AMD but Intel are certainly in a hurry to rectify the biggest bollocks they've ever dropped. i5 sixth gen minimum I would recommend.