Good choice of food to try out in Tokyo!

I haven't been to either, but I checked out the reviews on tabelog (the most reliable place for restaurant reviews in Japan).

Obana looks like the obviously better choice. Its rating is significantly higher, plus it's cheaper. Yamanochaya looks very formal and might not be as comfortable an experience for you (and you'd have to make a reservation). If you go to Obana, it might be better to show up right at the opening, at 11:30am, as they do not take reservations.