The first thing that you need to consider is the aspect of creative control. Creativity might be something that you very much value in your day-to-day interactions and in either field, you will find that it comes in handy. However, when you are looking at advertising, you will have complete creative control; because you are the one who is paying for the space, you will be able to put whatever you want into it. On the other hand, if you are working in public relations, you are going to have no control over how the media presents you, if they decide to use your information at all. Remember that the media does not owe you its attention and that you are going to have to work to get it.
This leads us to the issue of exposure. For instance, if your company pays for ad space, as with advertising, you are going to know exactly when your ad will air or get published. This means that you have a lot of control; an ad that appears during the Super Bowl is a lot different from an ad that appears late at night on the public access channel, for instance! On the other hand, if you are working in public relations, you are going to be in a place where you have to drum up interest from the media. Whether you are looking at news conferences, press releases, or even simply interviews, you are going to be dedicated towards getting good media exposure for your company and what it needs.
Also, consider what your operant time frame is going to be like in advertising versus public relations. When you are working in advertising, for example, you will find that you can run your ads as long as it is popular and as long as you have the money to do so. An ad that is really good, that will capture the public's attention and get you more sales can run for ages. On the other hand, the shelf life of a press release is going to be significantly more limited. You can submit a press release precisely once, though chances are good that you are going to be submitting it to a number of different outlets. Remember that an editor is going to want to see something fresh and new every time!
If you are contemplating the difference between public relations and advertising, you will discover that there is a lot of great information out there. Choose the career that sits well with you and make sure that you know all about it before you get invested!