When Kasem was DJ'ing, radio was at it's peak. New music was coming out constantly and the radio was the primary way that audiences were able to hear new music. Nowadays, people do not listen to the radio for new music, they mostly listen to drown out the silence of a car ride. Since radio is not as important to people these days, there doesn't need to be great DJ behind the radio station.
There are plenty of radio presenters that compare to Casey Kasem. All you need is a strong voice and thick skin. But whether or not he's better (and it always comes down to that) is a personal question. I like shock jocks and the attics they can pull so a radio presenter of any other kind just won't appeal to me. But that is just my opinion.
Kasem actually started a lot of the trends you see in modern-day radio, such as informational banter between songs. Today, radio's relevance is being challenged by the television and the Internet, so there are fewer avenues for a newcomer to make a major impact. I don't expect anyone to ever have the same effect on radio that Kasem did.
There aren't any radio personalities who are similar to Casey Kasem. Aside from being a good presenter in general, he had a very unique voice, which was part of the charm. As an example, prior to his death it wasn't known by many that he was actually the voice of Shaggy in the Scooby Doo series. Additionally, radio has changed from the times when Kasem was on it.