Having used (built) both one piece and 2 or 3 piece bodies:
The difference is that one looks better and doesn´t have a glue joint running through it. This is the ONLY difference, other than a one-piece body being more likely to warp if improperly dried.
BTW, Xero: when tap tuning, the pieces of wood are PURPOSELY matched in thirds or fourths by most luthiers. The reason behind this is that if all materialy had the same resonant tone, the result would be a so called "Wolf tone", a not that will ALWAYS overpower every other note, regardless of which octave it´s in (think of it as if you were to "tune" your trem springs to e, keeping the bridge position. The springs would go ballistic every time you play an e). So that particular combo (c and F) would almost certainly work well