Graham,
There is no sub woofer with the Peavey Messenger so there won't be as much bass, but the bass sounds tight and solid for the size speakers being used. I can't comment on the Logitech speakers because I've never heard them and compared to the Tyros setup, the Peavey has a warmer and louder output.
George Kaye
Kaye's Music Scene
Reseda, California