There are several differences between these two diuretics which may influence why they are given. Lasix is slightly older, being patented in 1962, versus Bumex, which came out in 1970. Bumex is more potent than Lasix at a concentration of 40:1, such that 1mg IV Bumex is generally equivalent to 40mg IV Lasix. Given orally, Bumex is better absorbed than Lasix, and also food does not impact the absorption, which makes it a little more predictable, and can sometimes be preferred for that reason. If a patient is not responding to IV Lasix, sometimes they will switch to Bumex simply because it's an alternative. Some older studies have shown that Lasix can be more potent than Bumex, and I've heard anecdotally that Lasix is "harder" on the kidney, although I didn't see that reflect 100% in the literature. Check UpToDate.com if you have a prescription at your institution. Generally speaking, there are not HUGE differences between the two. A lot of it comes down to personal practice of the physician and the hospital convention.