If you're looking at the master's as a stepping stone to the Ph.D., then don't do the U.S. ones. Or do them, but realize that they are very much professional degrees - training for practitioners in politics, not the study of politics. And no, Ph.D.s in poli sci in the U.S. usually don't require a Master's, although Fletcher is the exception to this (and a UK degree doesn't count as Master's for them).
And the U.S. does generally have more money, but that's usually reserved for Ph.D.s. A couple of my friends did get scholarships for their degrees in the U.S., but they did not cover everything. Given that UK degrees are only one year long (with the exception of Oxford), you'll likely pay somewhere near the same amount with a significant scholarship, but more than double if you don't get one.
Anyway, you asked about amounts. Talking about the professional schools, if you're coming straight out of uni with no work experience, don't expect any financial support. You'll have an easier time getting in since you're international, but let me put it this way. I've just applied for Ph.D.s, although for the reasons outlined above Tufts admitted me to their master's program. If I attend (and I won't), I'll have the LSE master's plus 6-7 years of work experience by the time I enroll. They gave me $22,000, excluding fellowship support. I have some savings which probably lowered the amount they gave me, but still, it's a measure of what they look for and how much they give. Other schools will naturally be different, though.
Now, if you are looking at Ph.D.s, you might be better served by applying directly. Again, support varies, but the school that I'm going to gave me $60,000 to cover both tuition expenses and a generous stipend. Plus, Ph.D.s in poli sci/IR look for different things: work experience isn't necessarily prized, and if you have good quantitative methodology skills, that's very valuable.