I've been researching that very question for a while, and have come up with a few conclusions. Of course, nothing is absolute, and everything is subject to change!
It's difficult to compare because of the relative youth of Oxford and Cambridge on the MBA scene. That being said, I agree with Ivan - they're about equivalent to US schools ranked 10-15, maybe 15-20 if you're a Europhobe
On the other hand, Oxford went up 3 places in BusinessWeek's ranking over the last year, and I expect that Said and Judge will join the ranks of LBS and INSEAD as the elite European schools within the next decade. Of course, I could be totally wrong, but I know that Said poached HBS's Dean and have been quietly fortifying their program for the last couple of years.
2. Placement Opportunities
Both Said and Judge do reasonably well on this front because of their proximity to London and their stronger-than-expected networks in the US and Asia. Granted, it's no H/S/W but I think it compares favorably to Stern, Darden, or Johnson. On the other hand, the European economy isn't all that great, and if your future is in North America, you might want to go to a US top-10 instead and save yourself the bother of moving!
3. Quality of Education
Oxbridge is synonymous with quality education. This will be true until 2+2 = 3. It's right up there with Harvard. Going to Said or Judge will give you access to a plethora of resources, as the undergrad and graduate disciplines are closely intertwined (more so than at US schools, by and large). Oxford, in particular, has a very strong finance department, and both Said and Judge place a special emphasis on entrepreneurship. On the other hand, if Marketing is your cup of tea, you may be better served at Kellogg. Similarly, if analytics is your field, you will love Booth/Sloan more. It all depends on what you want to get out of your MBA and where you want to go from there.
4. Exposure & Opportunities
Look - if you go to Said or Judge or a top-15 US b-school, you're gonna get more exposure and opportunity that you can handle. All of these schools have influential guest speakers and lecturers and academics and whatnot. All of them have a powerful alumni network (US b-schools because of strong MBA traditions, Oxbridge because ... well, because it's Oxbridge and one of their graduates is never too far away). If you look at the list of employers, you'll find eerie similarities between most top-notch b-schools. It's possible that US schools have more developed Career Services depts, but I don't know if that's always going to be the case.
In conclusion - this is not a Harvard vs. Kentucky Mountain State kinda argument (no offense to any Kentucky institution that goes by that name, if any). Oxbridge vs US is a difficult comparison, whose outcome depends entirely on the individual. Your career may be better served in one place or the other. Having said that, I highly doubt that going to one and not the other will lead to substantial missed opportunities. If you gain acceptance to one or more of these schools, you're doing very well for yourself and can expect to continue the upward trend.