Scala is compiled down to byte code and is statically typed so many of the same optimizations that can be done for statically typed languages like Java (as opposed to dynamically typed languages like Groovy) can be done. So comparing Groovy to Scala is comparing apples to oranges.
Now, Java to Scala comparison:
You can expect Scala to be on par with Java in most situations. Scala can be slow if you program in it stupidly, e.g., tones of mix-ins via Traits could provide some overhead that plain Java wouldn't have.
But ...
If the Traits are actually solving a complex problem in good taste, then a solution in plain Java would have to tackle that same complexity. Who's to say the solution you write in Java using your own patterns is going to be more efficient than what you get for free in Scala (remember, the Scala compiler was written by people that are probably a better programmer than you are).
On the other hand, if you are using language features for no good reason (e.g., Integer objects when plain int primitives will do), your code will be bloated, slow, crap no matter which language you use.
In addition, consider the special class of request-response based applications that interact with a database or other I/O intensive resource. The bottle neck is not going to be the 'new' operator or virtual method invocation overhead - it will almost certainly be the I/O.
In summary, performance between Scala and Java is about the same, and shouldn't be the biggest reason you choose one over the other in 99% of cases. Since skilled human labor is more expensive than computer hardware, you are better off choosing the language that you can (or can learn to) program most efficiently in (including your teammates). If Scala lets you write one tenth the code as Java, you might gain 10X the benefit by using it. If Scala slows you down 10 times (because it's too hard to read), stick with Java!