Most old-time tunes are fiddle tunes, with an "A" part and a "B" part that each repeat twice in a pattern of AABB, over and over again. There are many exceptions, but that is the basic pattern. In old time, everyone plays together, there are no "solo breaks," as in bluegrass. The fiddle generally carries the tune. The guitar generally carries the rhythm. The mando can have a great time, because it is generally free to play melody, harmony, counter-melody, rhythm, counter-ryhthm, percussion, etc, depending on the group and the talent of the mando player. Chop chords are only used as occasional "special effects. When mandos play rhythm, they more commonly play open chords, emphasizing the bass notes. There is singing in old-time, but not on every tune, and not all the way through even the tunes that there is singing on. There is more emphasis on communal singing, rather than intricate harmonies like there is in bluegrass. MHO of the key difference in the two genres, is that old-time is more of a "communal" experience of musicians relating to each other, whereas bluegrass is more of a "performance," even at a jam.
Because the mando isn't "locked in" to any role in old-time, it is a very "welcoming" genre for a newcomer, because you make whatever contribution to the music you can make, but no one is depending on you for a critical role. But at the advanced end, you have all those options I mentioned to experiment with to "spice up" the tune. Bluegrass is fine, but old-time mando is my passion.