The Dirty Pair are the ultimate Sci-Fi Female Duo and the relationship between Yuri and Kei is a wonderful and highly enjoyable Hate-Love relationship, Almost like the relationship between two siblings. The setting of the story is quite cyberpunk, akin to that of Akira for example except of course that Dirty Pair is a comedic series. It is soft Sci-Fi, and the futuristic setting and devices are never really explained but this doesn't mean that the Space battles and sci-fi technology fall flat. It is an old series, and the characters of Yuri and Kei will probably appear to be Bimbos at first, although there are many emotional scenes in the story that will make the Lovely Angels more human and enjoyable. Although the characters rarely show true affection for one another, the bond between the pair is really strong and the two put their life's on the line to save each other. By the end of the series the pair will have grown immensely and will become much more professional.
That being said, Dirty Pair is still a comedy and the Bimboish nature of Kei and Yuri is quite funny to watch as they are supposed to be highly professional Private Agents. The pair will at any opportunity try to blackmail or manipulate their superiors to give them a raise or longer vacation. This slightly unprofessional behavior leads to their unintended infamy as the Dirty Pair because they destroy things in their wake, although most of the destruction that follows in their wake is never really their fault. (Comedy ensues.)
Overall, this light hearted cyberpunk anime is very fun viewing and is perfect for relaxing over the holiday however the characters can at times be a bit simple. Don't take the series to seriously, after all the Fourth wall is broken at the end of each episode for the preview.