Had opportunity to sample both over the last 10 days, and we vote for Gypsy hands down. Excellent hummus, juicy lamb & organic chicken kabobs, chewy & flavorful pita bread, fluffy saffron rice & ultrafresh tabouleh albeit heavy on the onions. Both places are friendly with slow service & offer tasty food, but the Persian owners at Gypsy are more engaging, the atmosphere quieter, the food better IOHO & prices lower -- much lower for some items. Sandwiches < $5, entrees <$10. No alchohol license so BYOB.
Anyway, suggest you try both Gypsy & Sesame & then decide for youself.
Open for lunch continuously thru dinner every day, located next to Belmont Brewing off Ocean Ave.