If I'm picking just between the revolvers with no outside factors pushing their way in, I'm taking the 15 because I prefer the sight picture with the S&W adjustable rear sight. However... especially in my area, gondolas chock full of trade-in, LEO, DOC and other former issued guns have been filling the market for a bunch of years, so it's the Model 10's we see many more of.
I've got a pair of pre-Model 10's (one from 1921 & the other is a bit older), a nickel dash-6 from '83 with a 4-inch pencil barrel and a 4" heavy barrel 10-10 from '94 that was an Ohio Dept of Corrections gun with a thoroughly abused exterior. That gun is pure joy on a range day, and I tend to run it with a nasty 125gr load that I developed harsh on purpose for another very specific task. I wouldn't run that load in any other .38 Special, but I feed a heap of it to my ugly duck 10-10.
The two pictures you attached-- if I'm asked to pick ONE of them up and perform a task, it would absolutely be the Model 10, simply because of the Uncle Mike's rubber grip. The OEM wooden stocks on the Model 15 are attractive, but I can't help but wonder if the guy who designed them (and EVERYONE who agreed to let them be shipped out attached to revolver, for that matter) was any manner of a shooter. I'd rather shoot a Rohm with a proper grip than suffer through a gorgeous Model 15 with those as-issued classic (awful) stocks. My 10-6 was wearing them when I got it a handful of years back, and they were yanked off ASAFP.