This is what some people call "buying up" your education. (The term "buy up" refers to paying extra money to gain a degree from a more prestigious law school.) In my opinion, this is usually a bad idea-unless you have an unlimited supply of money, have no debt, and don't mind attending school for another year.
I feel that an LL.M. makes sense if you intend to specialize in a particular area of law and the LL.M. will provide you with unique knowledge that you could not gain elsewhere (or as quickly elsewhere).
I want to acknowledge that there are certainly numerous very good LL.M. programs that can help your career. (For example, an LL.M. in Tax is a prerequisite for many top tax practices.) Also, LL.M. programs can be very good options for experienced attorneys who want to further hone their education in a particular area of law. However, an LL.M. should not be used simply to buy up your education to a more prestigious school if you are not sure how relevant the LL.M. will be once you graduate.
I can tell you that employers focus much more on performance in law school than they do on performance in an LL.M. program. While an LL.M. diploma from a prestigious law school will certainly look nice on your wall, it is not the same as a J.D. diploma from a prestigious law school. Employers are not as impressed with LL.M.s since it is widely understood that LL.M. programs are generally easier to get into and not as competitive as law school.
In short, think carefully about investing additional money in an LL.M., because it in no way guarantees employment upon graduation. If you do decide to seriously consider an LL.M., be sure to speak to attorneys who (1) graduated from your (or a similarly situated) law school and (2) also earned LL.M.s from the same program you are considering. Ask if they are glad that they got their LL.M.s and whether, if they knew when they enrolled in the program what they know now, they would do it again. This should give you the best perspective.
Good luck, and thanks for the question (which many people have).