SpeedyMusig requires each signer to collect all n nonce pairs (Ri,Si) as input to the hash which determines how they are combined for the final nonce. Musig2 allows a single untrusted aggregator to collect the (Ri,Si) for all n signers and send only the aggregate (R,S) to each signer. So, SpeedyMusig requires O(n^2) communication, whereas Musig2 can be done in O(n) with a dedicated aggregator.
However, I am not sure the security is the same. SpeedyMusig says the signer much check the list (Ri,Si) to insure that no pair occurs more than once, in order for their security proof to be valid. If this check is also needed for Musig2, then the O(n) communication pattern would depend on the supposedly untrusted aggregator to do this correctly.
Musig2 uses more complicated public key aggregation, requiring n exponentiations, to solve the rogue key problem, whereas SpeedyMusig has simple key aggregation under Verified Key model. I am not sure if this interacts with the above issue somehow, or whether there is alternative security proof or some other aspect of operation that doesn't need the "no duplicates" assumption.
For myself, I would really like to combine these 2 approaches, using the O(n) nonce aggregation pattern of Musig2 but with the simple public key aggregation of SpeedyMusig.