Re: Which is more efficient
If you're worried about efficiency you're worried about the wrong thing. One of those will catch and consume the exception the other will let the exception propagate. Empty finally blocks serve no purpose at all :)
Re: Which is more efficient
If you want to do something with an exception - even ignore it, you'll need a catch regardless of performance. (which basically is only a factor if an exception occurs)
Re: Which is more efficient
The ConfigSectionHandler is your own class (I cannot find it anywhere)? Implenet a test method like SettingExists to test if the desired setting is there or not. Try-catch is intended to deal with unexpected conditions, but absence of the setting is expected, it is one of regular states, in which the setting can be, nothing expectional.
P.S. If I could advise you, never do empty catch block, at least log the exception, otherwise the exception is consumed and you could be in trouble while investigating why something goes wrong