The grammar rules say that 'either' or 'neither' are used to agree with a negative statement and 'also' and 'too' are used to agree with positive statements. But in informal language people often use 'also' and 'too' for negative agreement as well.. so grammatically the agreement to 'I can't have fun' would be a) I can't have fun either or b) Neither can I. But, 'I, too, can't', 'I, also, can't' or 'me neither' are often used.

I think... the first sentence sounds like you are telling the listener about yourself, whereas the second one sounds more like you're agreeing with whoever was talking (and will perhaps go on to talk about yourself). I may be thinking a little too deeply into this ^^' The difference, if any, is very very slight. =)

I would understand them both to mean exactly the same

They're the same thing (and have the same effect), I suppose.