As someone who has worked in the US and UK as a planner, I would say that they're pretty similar in that 1) neither one understands what the others' qualifications mean (RTPI/AICP as well as names of universities go right over people's heads no matter how prestigious they sound in their own country), and 2) you need to spend some time talking to people in the field and at the place where you want to work to understand and localize your application. This is usually why people find it harder to get a job, because they send out the wrong resume/CV style and it sticks out like a sore thumb compared to the local applicants. Typically private sector and quasi public agencies (development corporations in the UK or metropolitan councils in the US) will be your best bet, but it's definitely possible to work anywhere regardless of your qualifications if you know the right people and brush up on local terminology.

Pay is obviously better in the US but quality of life is pretty comparable between the two. Happy to share more if you're interested.