I don't know that it makes a difference in regards to the quality of your interpretation of a particular tune, but it sure makes you a more versatile musician. If you have the option of playing the same tune on a different instrument, it can make all the difference in a band where one of your instruments is already taken--instead of duplicating someone else (with the close-concentration and compromise that requires to ensure you're playing every odd phrase the same) you can add a whole different flavour. Or, just as useful, you don't have to switch instruments as often.

Finally, when you learn techniques that areusually specific to a particular instrument, they can often be applied on a different instrument to good effect. EG you can play mandolin-style tremolo on a guitar, and do other things to imitate mando sound (chop chords, play way up the neck) if someone else is playing a conventional guitar part. Also, you get used to particular intervals that are natural to finger on mandolin or fiddle--but you have to really work at it to get them on guitar!

W-O