Hey mbc,
You might wanna wait for the oppinion of someone who has actually done an MPhil/DPhil at one of those places, but here's what I've heard from various more or less reliable sources. Anyone else, please feel free to correct me.
Most of the MPhil's won't be the same as the masters you get on your way to the PhD in the US. They are actually separate degrees and will usually have a strong taught component in addition to the research. There are exceptions (there's a 100% research masters at Edinburgh), but afaik those are pretty rare. Secondly, it might be tough to get funding for an Mphil. Funding is definitely not guaranteed and unless you can get something like a Gates scholarship there's a good chance you'll have to cover at least part of the cost yourself.
Now, the DPhil (and btw, you don't necessarily need to get an MPhil first, though it might help). Here funding should be easier, but again not automatic or assured. Cambridge has a bit of a reputation of telling marginal accepts "sure, you can come over, but we can't guarantee funding".
It's true the median time for a DPhil is < 3.5 years. Theoretically you should be done in 3 years, with a maximum extra year of buffer mostly used to finish writing up. As an extra motivation, if you do get funding it tends to run out after 3.5 years, so if you really wanna take the full 4 the last 6 months are on your dime (which might explain the median finish time).
The cost of the shorter duration is less flexibility. You're pretty much expected to figure out what you're working on when you apply, get accepted by the prof you're gonna work with, go there and start working. People do switch their research focus sometimes, but it definitely shouldn't change by a large degree and probably not more than once.
Other than that, it seems pretty similar regarding work-load, publishing etc.
Btw. I'm pretty much the opposite of your situation. Finishing my undergrad at Edinburgh, probably gonna do an MPhil at Cambridge and would like to go to the US for a PhD.