Any lover of the English language should never be satisfied with just one dictionary in his library; all have their own strengths, weaknesses, peculiarities, biases and feel. Essentially, your decision rests between two ends of a spectrum: the Oxford English Dictionary and The American Heritage Dictionary -- regardless of which side of the pond you reside -- and a Webster's dictionary somewhere in the middle.
The AHD represents the cutting edge in American lexicography. It's hip, it's cool, and it's filled with color photos. It includes brand new verbs such as "google". It's a great book to sit down with and browse through for hours, and it is a lot of fun.
I use the American Heritage Dictionary quite a bit in my research, however I find myself asking the question; "what is the purpose of a dictionary?" Is it to preserve the English language and grammar or to simply be a repository of all the words and quirky expressions that are spoken? The AHD seems to be an advocate of the latter. Its "Our Living Language" usage notes give credence and validate dialect such as "y'all" (you all), "ax" (ask) and the continual overuse of "like" as being conversation filler. (It's not just for teenagers anymore!)
It is worthwhile to look through the list of people who comprise the Usage Panel on the American Heritage Dictionary, an eclectic (questionable?) mix of individuals to say the least: the late Carl Sagan, Molly Ivins, Robin Cooke M.D., and others including film critics, poets, and even radio commentators. Throughout the AHD there is a disconcerting acceptance of non-standard English and, as other reviewers have noted, a heavy amount of political correctness. Ultimately, this dictionary does a remarkable job of presenting current American English usage as spoken, for better or for worse.
At the opposite end of your dictionary purchase decision is the behemoth Oxford English Dictionary: the "Concise" version being comparable in size (and cost) to the American Heritage Dictionary. Here we have the keeper of our mother tongue, with a more stringent adherence to grammar -- some might say to the point of being stodgy. However, if you are concerned with the degradation of English and wish to preserve its usage and write "correctly", the OED is the better choice. Like the AHD, the Concise OED is a lot of fun to sit with and browse. Its many usage notes will clarify and take a stand on common confusions, such as "media" being a plural noun, whereas the American Heritage Dictionary seems to have given up fighting that battle and recognizes current vernacular. Which is right? I'm not sure. I like the flexibility of the AHD, but find myself referring to the OED just as often, especially in matters of grammar.
So my recommendation is to own both dictionaries if you are a true lover of English and are the type of geek like me who enjoys reading a dictionary without having anything in particular to look up. The AHD is a really cool book -- the color photos and layout make it more than worth the purchase price -- and it is on top of all language trends, slang, and dialects within the United States. The OED is to be revered and relished for its love of the language and its desire to preserve it.
Or, if you prefer, at times the American Heritage Dictionary seems flaky, and at times the Oxford English Dictionary seems stuffy.
And if you merely need to look up words from time-to-time and aren't interested in linguistic controversy, any of the Webster's line of dictionaries will make a fine, and more affordable choice.