Not an expert on Paris, but FWIW:
You might prefer the 6th.
I think the 6th is a bit more touristy—it’s closer to the central Paris sights, as you know, and the teens might like the energy even if you aren’t crazy about it. Restaurants will be plentiful.
The 10th looks beautiful, with the Canal, and also the restaurants there might not be quite as expensive.
We stayed in the 11th last spring and it was affordable and quiet, but you might require more activity.

This old post may help: http://www.eurotrip….

IMO, Paris is one place where Rick Steves has the right idea about where to stay: Rue Cler and nearby areas in the 7th arrondissement

Thanks for looking that up, Oldlady.
I had read the question as choosing between the 6th or the 10th!
(Had not yet finished my coffee.)

Since you haven’t gotten a response to your specific question, I’d decide based on the following, in this order:

1. Proximity of a Metro station to the specific apartment
2. Proximity of cafes, markets, etc. (Google earth might give you an idea of what the streets look like) to the specific apartment.
3. How close the specific apartment is to the center of town.
4. All things equal (particularly number 4 as the 15th is much larger than the 10th), I’d probably go for the 15th.

Thank you all for your help. After much thought and reading, I’ve decided to take the apartment that is 100 meters from Canal St. Martin. It seems to be an up and coming area, close to the metro, and walking distance to many places of interest.

Correct, most of the 10th arrondissement has undergone gentrification in recent years.

I read that even the northwestern end of the 10th arrondissement (around Gare du Nord) is being gentrified and cleaned up now. When I lived in Paris 8 years ago, the Gare du Nord area was very sketchy. I can’t personally confirm what it’s like today, but I guess I’ll find out in May of this year. You won’t be near Gare du Nord, however. You’ll be on the opposite end of the district, in the gentrified area.

The 15th, especially around the Eiffel Tower, is a heavily residential middle to upper-middle class area, and dead quiet at night.