Academic review of courses, from information available online:
Bath: Extremely strong analysis and algebra content throughout. Also some number theory (though only in year 3 for some reason), and topology, so you've got all the major bases covered. Somewhat of a lack of teaching you to program, from what I can tell (mostly just MATLAB). Force you to do statistics/probability into the second year (urgh). Overall, extremely strong course.
Edinburgh: Website very pretty, kinda shitty to use. Not as much information available. Much stronger programming element, with a variety of languages and some actual theory. First year mostly junk (since Scottish universities often accept people a year earlier, this is inevitable, ignore if on direct entry year 2). Even less number theory content. Much weaker analysis content. Very little algebra. Does have some interesting 4th/5th year courses. Vaguely OK course, but significantly weaker than Bath's