Hi Dave - well, I am not an expert on the internals, but since noone else is answering, will tell what I think, but take with a grain of salt... In design, I believe these two are virtually identical. In fact, I don't *think* there is much difference in basic mechanical design between any of the many S&W double action revolvers.
The 686 has, I believe the old style barrel. Some folks here get real worked up about the new two piece barrel. Personally, I don't get real worked up either way about it, and suspect for 99% of buyers, the difference is a nonissue.
As far as cylinder size between a 6 shot and 7 shot L-frame - I think it may be a bit bigger on the 7-shot yes. I saw a photo of the 619 (6-shot) vs 620:
...and it is a little bigger there.
Personally, I think the 620 is a little prettier with the half lug, but the 686P looks a bit more intimidating, and will have just a little less flip with that extra meat out there (I have the 4" 686P). Plus, if you're worked up about the two-piece barrel too, you'll sleep better with the knowledge that the construction method of your revolver has been in use for awhile.
Good luck,
Caleb