Higher speed = less noise and better specs in general. However, it gets more complicated than that.
You can push a Model 20/R-8 or E/G-16 harder @ 15 ips. You want to hit a machine as hard as you can without too much distortion to keep the noise floor down, which is still a factor with Dolby C, but especially important without noise reduction. Faster speed means more tape area for the same signal, which = lower disortion at a given flux level.
But dbx noise reduction allows a unit like the 388 to run at a lower flux level and still be pin-drop quite. dbx needs little help to do what it does. My 246 cassette portastudio is pin-drop quiet @ 3-3/4 ips and 160 nWb/m flux level.
Even though the 388 runs at a slower speed it still holds its own against the Fostex 1/4" 8-tracks.
The sound may be different, but saying better or worse is a subjective call.