Looking at your BTB vs the MM, there are some obvious physical differences:
- Weight matters. If the MM is a US model, it's probably a good pound lighter than the Ibby. Smaller and lighter always feels "friskier"- try a Beatle bass sometime!
- The longest fret-to-fret stretch you'll normally do (C to Eb on the B string, first position) is about an 1/8th of an inch longer on the Ibanez. Not huge, but still a small, noticeable difference.
- The BTB has a wide/flat neck carve, combined with wide string spacing at the nut and bridge. This neck shape (and the considerable size) make it best-suited to people who use a mechanically efficient, "classic guitar" fretting hand position: an open hand, the thumb fairly low, behind the neck.
- The MM has a rounder carve, with narrow spacing at the bridge and nut, and one less string. As a result, it's more forgiving of the typical "rock and roll" hand position, with the fingers curled in a more cramped shape and the thumb higher, possibly even wrapping over the top of the neck.
- Assuming that the MM is a US model, it's also a more expensive bass, and may show the effects of cleaner fretwork and a better setup.
- The MM may be using round-core strings (like DR Sunbeams), which feel a little softer and less stiff than typical hex-core strings, even when they are the same gauge.
- The MM may be using smoother strings (ie; most nickel strings vs most stainless), which can also be a little easier on the fingertips, plucking or fretting.
- A lot of players who own multiple basses, are particular about string spacing at the bridge. Particularly if you're a guitarist, even a small increase in string spacing can throw off your timing, making the instrument feel clumsy when you are jumping strings.