Obviously there is no "one size fits all" approach to game AI, at least not yet. There are a variety of different approaches and usually you choose one that is a good compromise between performance and control.
One increasingly popular approach, at least in shooter-style games is to use behaviour trees. These effectively give the same results as a hierarchical state machine except that instead of trying to control all the different transitions, you basically evaluate each behaviour node in turn until you find one that triggers, meaning that is the current state. The way you organise the tree lets you encode priorities, parallel behaviours, complex selection criteria, etc.
The downside is that they are basically a graphical language for AI rather than a single approach, and everybody codes them up slightly differently. On top of that, due to the naive approach requiring a lot of tree traversal, a lot of people try to optimise them by remembering where they were in the tree last time, adding external triggers to invalidate current states, etc. The majority of talks and papers on behaviour trees seem to be documenting the way that people twist them in unusual ways to get better results, so I'm not convinced that they're all that great.
But lots of people do manage ok with hierarchical state machines. As long as you have a clearly delineated hierarchy (eg. game objective/strategy/tactics/navigation/steering) it's not impractical. The hierarchical nature is meant to prevent the exponential growth, so you might want to reconsider your transitions.
In fact you can get a long way with a trivial set of conditions. eg. If healthy and no enemies nearby, explore. If healthy and enemies nearby, attack. If unhealthy and enemies nearby, flee. If unhealthy and enemies not nearby, apply health pack. 4 basic states, no explicit transitions, and easy to tweak or personalise by adjusting the definitions of healthy and nearby.
Nobody (or next to nobody) uses neural networks, by the way. They're not a very effective tool, except for learning basic AI concepts.