I have a friend who was in your position last year. He had a maths offer from Cambridge and a Harvard College offer. He went for Harvard because he liked the international aspect of it and also he liked the flexibility of the course. Everyone always saw him as the maths guy, but he was interested in politics and philosophy as well and Harvard lets him explore those subjects, though obviously his maths training is less in depth.
That's quite a big consideration (besides the massive decision of living abroad) - do you think you'd enjoy studying engineering to a great depth from the very start? (If so, Cambridge would cater to this better I think) Or do you think you'd like to explore other routes?
Also, it's cheaper for him to study at Harvard because they pay for everything and this is despite the fact that had he gone to Cambridge he would have paid the lower fees of £3000 (though this money is on the condition that he works part time for the university in some capacity)