I'd probably say it's best to write on whatever you are comfortable in using. An accoustic for writing is great but it all depends on
what you are writing. These days it's all been done so the trick is to present your song in a different way. So now it's all about syncopation and harmony.
It's much better to work high up on the fretboard, finding your triads and working from there, rather than at the top of the neck playing the tired
and worn out C G Am F chords in the normal manner. Unless you are writing "another" accoustic only song.
Different instruments take up different layers. If you wrote a piece on a piano you could easily work out the Viola, chello, violin, brass parts because they all take up
a different space. The viola's would be pretty high up the scale whilst other instruments take up lower parts. Stick those bog standard shapes in on the guitar and often they won't work.
I guess it also depends on what type of music you write too. I would think if you are intending to write a thrash metal song then you will want to hear all that reverb and
distortion and so on to better help you feel in the right mood for writing that kind of song.
Personally I choose whichever instrument I think will better help me write the kind of song I intend to write. If I don't know what I intend to write then I usually play on all of them
until I find somthing I like