CUDA is a data parallel programming model for what is effectively an SIMD architecture, so obviously it isn't as flexible as a general purpose multithreaded or MIMD architecture. Certainly kernels can be a lot more complex than simple arithmetic operations.
In my own work I use CUDA a lot for solving partial differential equations (so the finite element, finite difference and finite volume methods), which every thread processes a cell or element from a discretised continuum. In that sort of calculation, there are a lot of FLOPs per thread per cell/element.
The key area to be mindful of is branch divergence. Because it is an SIMD architecture under the hood, code where there is a lot of branching within a warp of threads (which is effectively the SIMD width), will suffer performance penalties. But branch divergence and code complexity need not be synonymous, you can write very "branchy" and "loopy" code which will run well, as long as threads within any given warp don't diverge too often. In FLOP and IOP heavy algorithms, that is usually not too hard to achieve.