Scratching that Streets of Rage or Final Fight vibe with something NEW is usually a challenge. Luckily there’s a game for you. World Heroes Supreme Justice Extra does exactly that, and has special moves that are akin to Street Fighter. (Down forward punch, down forward kick, etc.)
Check out a video on the game that I put together here, utilizing the female characters of the game:
And if you want to download the game for yourself, you can find the link here.