First, Cassandra uses a disk layout similar to the one described in the Bigtable paper (http://labs.google.com/papers/bigtable.html sections 5.3 and 5.4); in particular it does no random writes. Relational databases like mysql pretty much all use btree-based storage which was great 20 years ago but is terrible today when seeks are your bottleneck.
I was talking to some people today who are struggling to get mysql to do ~100 insert/update operations per second. Cassandra will easily give you 10x that -- _per node_.
The second benefit is that Cassandra gives you real, scalable partitioning, invisible to the app, for when you do need to add nodes. When you have more than a handful of machines, not having to babysit replication + partitioning is a huge, huge deal.