What are some of the big differences between functional programming vs. object-oriented programming?

Well object oriented programming is nice because it allows you to model your complex problem into hierarchies so you can simplify the problem. But it becomes very hard when you start to consider multi threaded programming while using mutable objects. In such cases you need to use heavy use of synchronization objects and it's near impossible to perfect a large application.

That's where functional programming comes in. Because of things like immutability functional programming really simplifies multi threaded programs. It makes it almost trivially easy to parallelize something when you know that given input X to a function it will always output Y. Also you know that a variable (or value in functional programming) can't change mid use from another thread.

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Functional programming is based on a declarative model and has its roots from lambda calculus. It offers a lot of great concepts which can be borrowed from more imperative languages like C++ and C#.

Some examples include referential transparency, lambda functions, first class functions, lazy and eager evaluation, and immutability.

If for nothing else learning functional programming is useful for the concepts that it contains. It will change the way you do programming and think about programming. And I would guess that in the future functional programming will be just as important as object oriented programming has been.