The main difference you will probably notice pertains to addressing the computer memory, through pointers and through manual memory allocation/deallocation.

In a broad sense, Java is pretty similar to C. I think if you wanted a perspective-altering experience, learn something like Lisp or Haskell. But I agree that there is value in learning C. You should probably learn both C, and Lisp or Haskell or Scheme or whatever functional-ish language looks interesting.

(This is with the assumed goal of getting an overview of programming language styles. If you have specific application-building demands, then language choice may be more dictated by that, e.g., Objective-C for iOS.)