"Too bad", as above -- I feel that context and precise wording, come into play here. It would strike me that "That's too bad" -- whether from a Yank or a Brit -- would imply sympathy and commiseration; whereas just "Too bad !" implies indeed, as above, "Tough luck, it serves you right..." / "my poor little heart bleeds for you", and similar snarky comments. Could it be that Americans don't use "Too bad !" thus, in the snarky sense -- with them, it's always the sympathetic "that's too bad"; whereas Britons use both, varying according to their sentiments vis-a-vis the person and their misfortune?