It is statistically harder to get into not just Oxbridge, but any of the more selective English universities if you study in Scotland. The reason for this is not that theres any favourtism or the exams are harder, but, as ixivxivi says, more to do with the education system post highers. If you are at a selective private school, you'll have little problem with at least giving it a shot, as advanced highers run in almost all subjects, and the support is there to take 3 or 4 of them. The problem arises at state schools, where (in my experience) advanced highers were only available in the larger depts, and subject to demand. Therefore, for a budding historian at a Scottish state school like the one I attended, the only advanced higher they could do (assuming maths, the sciences or another language wasn't their forte) was English- providing at least 10 people wanted to do it. So, while this student may have had 7As at higher, having just one advanced higher rules out England.
However, this doesn't apply to every school- and while most students aren't in a position to sit three advanced highers, a significant chunk are, and won't be disadvantaged at Oxbridge because of it. The other thing to watch out for, which doesn't happen in England, is the way the system acts as a distraction to advanced higher students. In England, everyone in A-Level who has serious intentions of university is working their behinds off to achieve their grades. In Scotland, since the Scottish universities accept highers, you may find most of the year have offers at three or four very good Scottish institutions, and are now picking up the odd subject to avoid getting a job, and are intent on having fun for their final year. When 10 people have to work to get an A in Adv Higher, its not always the easiest when the other 90 are already into their courses and are having house parties every weekend. Since most Scots won't persevere with adv higher unless they want to go to one of about four English universities (or gain entry to second year in Scotland), then a good few decide enough is enough and take their (often unconditional) offers up at Gla/Edin/St Andrews and the like.
In short, it can be done, and in some schools you'll have more chance than others, but it won't be easy, or without its complications.