Photoshop and Illustrator are two very different graphic programs.  They are both powerful tools for graphic designers.  They both share many of the same characteristics and most designers use both.  They are meant to compliment one another so therefore one is not better than the other.

In terms of which is better for logos.  When determining which program is better, you have to know the fundamental differences between the two programs.  Photoshop is a bitmap image processing application.  This means that Photoshop works on individual pixels.  Illustrator on the other hand is a vector based app.  Vector based application is just a fancy term for using mathematics to draw lines.  The advantage to this is that a vector based image is scalable.  You can draw something an inch wide or blow it up to a mile if you could.  A bitmap image that’s blown up will look pixilated. 

In knowing the differences between the two, most designers would prefer to use Illustrator to design a logo.  The end user wouldn’t have any problems with resizing the image without having to worry about pixilation as the image can scale bigger or smaller without and degradation. 

Which one should you use?  Well it really comes down to where you’ll be using the final images.  If you’re going to be using the images for webpages only, then you can use Photoshop because you don’t have to worry about scaling and you can create some really great effects.  However, if you’re going to use the images for web and print, then you’re probably better off using Illustrator for the sole purpose of scalability of the images without blurring.