Edit: It guess I was wrong as mentioned in the comment below. Here is a possible answer: Obama can't have an iPhone. The reason might (not) surprise you! (+video)
Original Answer: I don't think it has to with Blackberry security specifically. Secret service could get any phone secure enough to be used by the president.
It has more to do with the preference of Obama. He used Blackberry long before he became president and he doesn't want to learn a new operating system or phone all over again, the same way I don't use Windows 8, or upcoming 10. I don't want to learn a new operating system when the old one works just fine or even better than the new one. Newer is not always better.