Convention for most currencies is flat compounding. This includes the most liquid G4 basis swaps:
EUR 3m vs 6m, 3m vs 12m, 1m vs 3m
USD 1m vs 3m, 3m vs 6m
GBP 3m vs 6m, 1m vs 3m
JPY 3m vs 6m, 1m vs 6m, 1m vs 3m
Typically the spread is quoted in terms of the leg with the shorter tenor.
Two notable exceptions are EONIA v 3m and the (relatively new) SOFR ...