With this new info, I think half the previous replies are obsolete. This was important info...
Since your daughter's daughter has a 637 that your daughter has been able to shoot, and shoots fine with ammo that is well matched to the gun, a lot of the previous replies (assuming little to no experience with a lightweight snub) aren't really accurate.
With this new info, I'd say either should work for your daughter if that is what she wants. As for the 637 vs. 642, that is just a matter of preference. They are essentially different versions of the same gun, the 637 being a more traditional DA revolver with a hammer that can be cocked for SA fire, and the 642 being the DAO Centennial with a concealed hammer. The weight is the same (or nearly so), both are S&W, both aluminum... Other than DAO vs. DA with a hammer, there really isn't a difference.
I have a 442 (basically the same as the 642, just a different color) and a Taurus 856UL. In this case there is a slight difference in shooting comfort, but the 6 shot Taurus has a little more metal and is a little heavier as a result, and it also has a more hand filling rubber grip vs. the thin wood boot grips that came with the 442 (the 442 is also more comfortable with different grips than those it usually wears). Where I do have a big difference in comfort, and the 642 will likely have over the 637, is IWB or even belt carry without an undershirt. The hammer of the 856UL can dig into my side at times, where the smooth corners of the 442 carries more comfortably than just about any other gun I own. So, how does your daughter plan to carry? If in a purse or pocket that won't matter as much for comfort (though the 642 is more snag free), if IWB or on a belt without something between the gun and her side, it can make a big difference.