Runs really well, the music is great. I have a TG-16 and Turbo Everdrive but no Turbo Tap. Gameplay feels exactly like the NES.
Issues: The sound effect for the grenades is not great, nor explosions. In the game music, anything that is drum/percussion heavy seems to have a popping sound. Screen scrolling occasionally gets a single black horizontal/vertical line for a second. Lastly, when scrolling, the "ground" seems to get a lot more blurry than the NES version.
Frankly, this is amazingly close to the NES, though I can't test 2P mode, and I feel a huge improvement musically over your Contra port. The music (beyond the drums) is an improvement over NES thanks to better TG hardware.
PS: I compared my results to using Magic Engine on PC. On the emulator, the scrolling seems fine, no blurriness, with occasional screen glitches. Percussion isn't as distorted/popping. FWIW, I used TurboBooster composite out directly to HDTV, which looks like shit. Then used it with my DVDO upscaler, which cleans it up nearly perfectly. Still has the glitches I mentioned.
Lastly, I hooked up the TG to an old CRT, and the blurriness in the background scrolling seems much better, so could just be the LCD TV's crappy deinterlacing.