This might be a little hard to compare, because, as others have said, Clojure's vectors have different goals from Java arrays, with persistence being the most important one, and the one at the core of Clojure's entire philosophy.

Persistent data structures do have performance costs that are probably significant. First, each "modification" generates garbage; garbage on the JVM has different collection costs – from virtually nonexistent to quite significant – but persistent DS might generate the most expensive kind of garbage: medium-duration-lived objects. The second is caching effects. Mutable data structures reuse cache lines, while persistent DS cause cache faults and pollute the cache. Clojure's transients help with that. Of course, persistence is an essential element of Clojure's beautiful values-and-states philosophy, so you do get something extremely valuable in exchange for some performance cost.

There's another issue with persistent DS: they can't be concurrently modified; they allow only one writer at a time. Clojure does support parallel modification using the very elegant reducers, but these only apply in data-parallel situations – not general concurrency.