(i think this is the right category; please correct me)
I usually use the former if I don’t need to reuse the function given to Connect. I think extracting the function really doesn’t do much (i suppose for extracting a long function? i don’t see the point in that either).
The second way is needed if you want to call the method yourself, as well as it being connected to a signal. If you don’t want to call the method you’ve connected, the first way is better for organization, but they perform the same either way.
I usually use the second option when there’s an extra level of complexity involved. For example having a list of functions that will connect to the event given a state, or a function that connects to multiple events. If something is simple in nature I tend to use the first option instead.
First way: only if I need to run snippet of code once or if it’s in a for loop.
Second way: If I need to use the function multiple times, or in more rare cases, when I need to initialize an object with the function before it can be updated by the same function. I mostly use it in Module Scripts. An example is notifyPlayer(message, color, sound) for when I want to notify the player with a popup or something.