In this case, go with option B. The unelided sentence is "This is more serious than people think [it is]."
By adding "what", you're introducing a relative clause, which is supposed to add more information. But you don't need further clarification, you need just a simple comparison.
Option A isn't "grammatically" incorrect, but it doesn't mean the same thing as B. Instead, the comparison isn't on how serious people think something is, but on what their thoughts are. Written out logically, option A means that this
is a more serious thing than whatever it is that people are thinking
. It's their thoughts that are less serious, not that they underestimate the seriousness of whatever this
is.