I am aware of three (!) English translations of the Mishnah, there is the Philip Blackman translation, the Danby translation and the Jacob Neusner translation.
How do these three translations differ?
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This seems more like an opinion piece than an actual question-and-answer thing, but for what it's worth I think that Danby's translation greatly overshadows Neusner's, but have not seen Blackman's (nor any other).
Danby translates the whole Mishna himself, is slavishly faithful to the Hebrew, and although he sometimes notes alternative interpretations in his footnotes, tends to rule like Rav Ovadiah of Bertinoro. Neusner, on the other hand, translated only part of the Mishna, the rest being done by his students. As a result, I find the overall composition sloppy and inconsistent, his preference for transliterating certain words (like ma'aseh) irritates me, and it's never succeeded (for me) in actually clarifying the text.
Fortunately, since I can read Kehati in Hebrew, I haven't needed to rely on an English translation, but one area in which I find it very useful - and would recommend Danby even for people who are confident with Hebrew - is when it comes to names of plants, or types of equipment, etc. Most of the time, Kehati is helpful in explaining what they look like or what they do, and while a good dictionary can be handy as well, seeing Danby's English translation and then looking it up on Google has helped immensely with clarifying for me exactly what some of these things are.