They both give the exact same information - (some) vehicles will be too high to pass under the bridge. Both are grammatically correct. They simply differ in the grammatical structure at the end. In the first sentence we are told for which vehicles there is not much clearance (those passing under) / when there is not much clearance (when they are passing under). In the second sentence, we are told what action 'not much clearance' prevents. It makes little difference. The information is the same. However, neither is incredibly precise or useful. Which vehicles? All of them? Both would be better if 'vehicles' were modified - high vehicles maybe.

I would say that the best one is the second one. It means that vehicles have it tough while being on that part of the way (under the bridge). The same could be said by "There is not much clearance for passing vehicles under this bridge". The first seems ambiguous. It could either mean exactly the same or not. If you were trying to say something like "the vehicles encounter difficulties right after crossing that section" then you would need a sentence more similar to the first one: "There is not much clearance for vehicles passed under the bridge"or even better: "There is not much clearance for vehicles past this bridge". The last thing I can come with is: "There is not much clearance for vehicles when passing under this bridge" which I would find quite equivalent to the second one you wrote.