EU citizen here, went to SGU, matched into US.
As far as US is concerned, you're in the same boat as any other visa-applicant. That's a big disadvantage during the match, but not a complete death sentence (anything that you read about Canadians struggling in the match will pertain to you!). It also requires annoying paperwork and a hateful realtionship with US bureaucracy at times of travels for clinicals. If you match, you will require to get a "statement of need" from the UK in order to get a J1 visa (which is what most visa-residents have in the US, as H1B work visas are not sponsored by most residency programs). I am not from UK, so I am not sure what getting a SON entails there. A statement of need can be a simple paper you get from some pencil-pusher in a ministry in 30 minutes (most of Europe), a stressful first-come-first-served competition for a limited commodity (eg. Canada) or a deadly NO that ruins hopes and lives (eg. South Korea). Check it before you apply.
You will have some advantage over the hardcore IMGs like myself by the virtue of speaking proper English. I speak peasant English with a thick off-the-boat accent and can't broadcast Beowulf references right and left, so that didn't help at all.
So, in the end, coming to SGU as an EU citizen makes sense mostly if you're going for the US residency. If you plan on staying in the UK, there are cheaper options in continental Europe.