Supposing we were to revise the question to be a choice between $1,000,000 or, say, 100,000,000 pennies (equivalent amounts of money) I'd have to go with the check for a million since pennies are pretty much useless en masse(save for
pissing people off).
However, say we up the game and and offer a choice between $1,000,000 and 1,000,000,000 pennies (10 times the value in cash, but now you're stuck with a
school bus size stack of the things). By the rules of the game, the only real restriction is that we can't exchange them for more sane types of currency. There is no restriction, however, on converting them from their current form to their component metals! Melted down, most pennies currently contain 97.5% zinc. At the current going rate of around
82 cents per pound, the school bus size stack yields 6 million pounds of zinc or just shy of $5 million worth of metal. Another $500,000 for the copper and you've got a grand total of $5.5 million.
Granted, that's half of what it was initially worth and you've probably expended a colossal amount of time and money to do this, but I think you'd still come out ahead of both the million dollars straight or finding a way to spend a billion pennies.