The belly mount system is just a way to create a forward handle, which for many adds to the pointability of the bow and stability at full draw. The Hill Country 3pc longbows are superb shooters, quiet and built with heirloom quality. I cannot speak for Rainy Day but I have heard only good things. The ultimate longbow in this configuration is the Habu Vyperkahn, several of which I have owned, but the Hill Country bows give nothing up.
The 1 and 2pc equivalents of this type of design would be your Shrew and Javaman style bows, and with the addition of higher mass riser materials and/or Bow Bolt system you can have almost the equivalent stability of the 3pc iterations. So that would keep your options open to a degree.
Really it comes down to the person behind the string. I shoot back or belly mount setups equally well myself.