What graph do you most recommend?

I recently read that Navmesh / Recast graphs are not particularly great when it comes to accuracy, even when working with multiple layers like bridges. They apparently are also harder to work with when trying to tag certain areas within them dynamically (like a trap or puddle of water on the ground as something to avoid). It seems that perhaps layered grid graphs are the way to go if you have some processing power to spare. Do you agree, Aron?

Depends on what you mean by accuracy.
Usually I recommend recast graphs over grid graphs because they can get more detail into the graph with only a relatively small number of nodes.
Layered grid graphs are easier to use and (usually) faster to update (this depends on a lot of factors though, so it is hard to say, navmesh cutting can often be faster than updating a grid graph).

If you are tagging certain areas dynamically, or in any way using different movement penalties for different regions then I would recommend a grid graph however. The reason is that it is very hard for the pathfinding system to estimate costs since pathfinding is done on the centers of the triangles (nodes) in the graph and they can have a very large variation in size. Therefore penalties will be much more accurate on grid based graphs.
Another downside with navmesh based graphs is that you can only apply penalties to whole nodes, and since the nodes are large this may not line up with the region that you want to change the penalty/tag of.