In very simple terms, each ICAO member state issues licences (be they PPL, CPL, ATPL) under its own national regulations. Within Europe, countries that are JAA (or EASA) members issue licences that are also JAA / EASA compliant. In other words, a PPL issued here will be a UK / JAA licence, while one issued in Florida will be issued by the US FAA (and will follow a slightly different training syllabus). To complicate things slightly, some schools in America also offer JAA PPL training, meaning that you would follow the JAA training syllabus and be issued with a JAA PPL at the end of it. Confused?
To build hours in the US you would need some sort of FAA licence, but it always used to be possible to get a 'pilot certificate' issued simply by presenting your UK licence. The situation has not changed to my knowledge, but you'd be well advised to check the latest position with the CAA and the FAA before committing yourself. It should, however, be perfectly possibly to convert a UK PPL and build hours in the US.
Comparing the pros and cons of the two systems is a great way of starting a willy-measuring contest, but rest assured there are significant differences. Having trained in the UK, with JAA and FAA PPLs and some hours-building in Florida, I would say that the US system is much more practical and common-sense based, while the CAA is more conservative, theory-based and wedded to the map and stopwatch (which most people bin as soon as they discover GPS). Regardless, to focus on your objective - airline employment in the UK, you will at some stage need to pass UK CPL and IR skills tests. Others will have different opinions, but I would suggest that the best foundation for that is a UK issued PPL. I do know people who completed all their training outside the UK and are now flying airliners, but I've also met people with JAA PPLs issued in Florida, who really struggled with flying to CPL standard. Essentially they were having to learn techniques from scratch, which is very expensive with a commercial instructor sat next to you.
I can well understand the temptation to escape the UK weather, but familiarity with our climate is all useful experience. (My CPL skills test was in poor visibility with a low cloudbase - perfectly legal, but not ideal when you're used to gin-clear conditions). I was surprised by just how steep the learning curve was with both the CPL and IR, and you really do want as many things on your side as possible. I'd suggest that maximum exposure to UK airspace, geography, RT and weather - before you start spending £300+ an hour - is a good idea.