Buying sports equipment will always be down to personal preference but there are a few general principles to be taken into consideration when buying running shorts for men or for women.
On the whole, mens running shorts are often looser fitting than those for women. This is generally for aesthetic purposes but both loose and tight fitting shorts can work, provided they are of the right kind.
Close fitting or compression shorts are good provided that they allow flexibility and do not cause you to overheat or sweat. Synthetics such as lycra running shorts and derivatives thereof, can help increase performance by creating less wind resistance than loose fitting shorts. In addition, they can help muscles to perform more efficiently by adding elastic support.
In cold conditions lycra style shorts may also help your muscles to warm up and maintain temperature more effectively but they will also dry quickly and wick moisture, in the form of sweat, away from the skin which is beneficial in both hot and cold conditions.
Alternatively, some will prefer loose fitting shorts. As long as they are not overly long, these kinds of shorts will not chafe the skin and will offer unrivalled freedom of movement. Additionally, they can also be worn over a close fitting thermal layer, for cold conditions.
In the end it comes down to what is comfortable for you. Hopefully this information will help you to choose wisely. Enjoy your running!