I think one of the really cool things about playing in this family of instruments is that there are fewer clear standards about how to play... the field is wide open for experimentation, and each player sounds different based on the combination of her/his instrument, technique, ear, hands, etc.
I turned to the large mandos because I wanted to play melody and rhythm (not just chop chords)... I am just getting my feet under me in this dept. With my Trillium (22.5" scale), some of melodies are too much of a stretch for me, so I look for counter melodies, harmonies, alternate fingerings, etc. Or I look for a more simplified way to play the melody. Or I skip a note and let it be implied or covered by another player. I do have small hands, and sometimes that means I have to move quickly up and down the neck. I may ultimately go to a shorter scale.
In terms of rhythm, I'd echo much of what has been said above. We have been over-trained to think of rhythm in simplistic terms-- boom, CHICK, boom, CHICK. For some forms of music, this is fine. But so much of what we play on mando family instruments has so much more going on rhythmically that there are many more options.
Rhythm playing is not the same as playing chords, necessarily. A good drone, played with strategic accents, can provide excellent rhythmic backup- for instance. Some understanding of polyrhythms can be very helpful in terms of figuring out how to place single notes or 2-note chords in ways that support or augment the rhythm of a piece.
And, of course, the "weaving" or crosspicking techniques are well worth learning...
Otter OM #1
Brian Dean OM #32
Old Wave Mandola #372
Phoenix Neoclassical #256
If you're gonna walk on thin ice, you might as well dance!