The fastest way to cross the Solent between Cowes and Southampton is the Red Jet.  These catamarans have replaced the hydrofoil service that was the quickest way over when I lived in Cowes.  The hydrofoils were interesting to ride on, particularly when the weather got a bit rough, and they had a single prop that, if they threw it off, left them bobbing out in the water awaiting a tow.  The RedJets are clearly bigger and probably a lot more reliable while still being fast.  I have never ridden on them but my family do frequently.