Finz is a Seafood & Grill place in Dedham and Salem, you meant "Fin's." Finz has had some adds recently on television.
I haven’t been to Asahi (I picked up a menu but never went).
I go to Fin’s often enough to be a “regular.” Before Fin’s opened I used to go to Kayuga near the Shaw’s on Comm Ave in Allston.
Fin’s has a good variety of rolls and I must say everything I’ve had has been excellent. The Sashimi cuts are nice and big and seem to be priced on par with other local sushi places.
I’ve been to Oishi in Chestnut Hill once and didn’t understand the hype. I thought it was fine, but nothing so amazing.
Another nice thing about Fin’s is that they have a very nice dining room. Nothing too fancy, but a couple of dozen tables, which one often doesn’t find (plus you don’t feel like you’re at a take-out place like one does at Oishi and Asai and others in the area). Also they completely gut renovated the place after the Chinese restaurant left so there is a nice, modern ambiance.
Finally, Fin’s has a liquor license (got it a couple of months after opening) so they have Sake (I’m not sure if they have hard liquor).
I really like Asahi as a neighborhood sushi bar. it's quite similar to places in Japan in size (read hole in the wall) and the quality and value are good. Fish is fresh and properly matched to the amount of rice. I haven't been to Oishii but from posts here, it seems more upscale and creative and pricier. I don;t know Finz.