In the statically compiled languages that most people think of when they hear "OO" (C++ and Java), yeah, switch statements vs. virtual methods (performance differences aside) is basically a matter of code style (do you want to organize by function/method, or by type/object?)
However, the original proponents of OO intended it to be used in dynamically compiled languages where it could be used as a way to implement open/extensible systems. For instance, if a game entity has true update, animate, etc. methods, then anyone can implement new entities at run time; level designers can create one-off entities for certain levels, modders can pervasively modify behaviors without needing the full source code, programmers trying to debug some code can easily update methods while the game is still running, etc. You can get a similar effect in C or C++ with dynamic linking (Quake 2 did this for some large subsystems), but it's a pain and kinda breaks down at fine (entity-level) granularity.
The other, "dual" (I think I'm using that word correctly?) approach famously used by emacs is to create hooks that users can register their own functions with, and extend the program that way. Like switch statements, it basically amounts to storing functions at the call site instead of inside the object, except with an extensible data structure rather than burning everything directly into the machine code.
Obviously you can't really take advantage of any of this if you're writing some state of the art hyper-optimized rendering code or whatever like Carmack, I'm just saying that OO's defining characteristics make a lot more sense when you drift away from C++ back to its early days at Xerox PARC.