This is a very touchy, sensitive subject. If your serious about your career I suggest you research both groups for awhile, and find out which one is right for you. There is also SESAC which is the smallest association. There is also PRS. And probably some others.
You should also look into Harry Fox, for Mechanical Licensing if your doing any major production or are dealing with label attention with your beats or music.
http://www.harryfox.com/index.jsp
BMI, ASCAP, SESAC, these only pay you for certain use, such as live performance of your music, live shows, broadcast/radio, and so forth. These companies pay you performance royalties. They do not pay you points (percentage of royalties) on record sales. This is by a Mechanical License between you and a label. Harry Fox is how you get that mechanical money, they collect it for you from the label, they take their percentage, and you get paid fairly, that big money. Harry Fox basically protects you from these labels, and prevents you from getting raped, and allows you to collect your fair share.
Back to performance royalties,
The way the tracking systems work are very complex. I mean, ASCAP is the oldest, and the system they use today, is the same system they used ages ago, I am talking probably the same system in the 1930's. You get paid based on very specific settings, dated back to when the company founded it's reputation. I mean it's the 21st century and ASCAP is using techniques that control/base how you get paid and how much you get paid that date back to the stone ages. A lot of people go with BMI because BMI offers a slightly larger broadcast "sample". However you can ask anyone signed under both groups one as writer one as publisher and the payments they get are virtually the same. Unless your making hits, serious hits, your not going to see much from either company to be honest. But it's still important to protect your music and your rights to get paid, even if these companies ASCAP or BMI, pay you pennies.
Research the companies. They do have differences, and those differences should be compared by you.