My thoughts for what it's worth...
The design is so simple it can be a bit "plain" to me which is how I feel about the 15mm. Even before I got the 19mm, I always felt 'is this it?" when I wore the 15mm.
Because it is such a simple and clean (e.g. plain) design, I like the larger 19mm size for nice pop of color. As I mentioned earlier, I never wear the 15mm anymore. It just sits in my jewelry tray. I was going to get rid of it, but my husband thought I was nuts since he knew how hard it was to find. Hence, I was pressured by him to keep it!

Jewelry is all preference of course, and you may love the 15mm.
For peace of mind... I would definitely order the 19mm and try on both to see which you prefer.
Good luck!