For years, Illustrator has been the ugly brother to Photoshop, (And it still largely is) - designers everywhere would get frustrated with Illustrators 'alternative' work flow when doing the simplest of tasks that would take seconds in Photoshop. - but in the last few years, Adobe have worked hard to make the unique abilities of Illustrator come to the fore.
It's not the ubiquitous image editing powerhouse that is Photoshop, and it's not trying to be. What Illustrator has become is the designers best friend. It has a layer of accuracy that isn't in Photoshop, you can design logos, layouts, text, fonts, anything using Illustrators methods and produce things that can be rendered at any resolution because of it's mathematical vector output.
As software developers, the world is becoming more and more resolution agnostic, every bit of software we make must work on multiple different display resolutions. From tiny mobile phones to gigantic televisions.
If we were to create our user interfaces using photoshops rasterised bitmap output, we would be forever making different resolution sized files. But with illustrator, (when you know what you're doing) - you simply need one file and the use of it's amazing exporting abilities.
The learning curve (pun intended) of Illustrator is steep. Much more steep if you've come from Adobes other amazing image manipulation software Adobe Photoshop.
For years, the layout of Illustrator, and the subtle UX interface differences has alienated its use for the beginning user, but once you get over the learning curve and the hurdles of "simply finding the right button" - it all starts to click, layers, and masks, and paths all become normal and then a world of accurate design is opened up. Making things that would take a long time in Photoshop a simple task in Illustrator (circular paths, for example, or pattern making are done so much easier in Illustrator than could ever be achieved in Photoshop) -
The best of both worlds (bitmap and vector) is to become proficient in both, but one area Adobe could look at is making Illustrator more uniform with Photoshop in it's way of presenting its user interface. There are *so many* inconsistencies between the two brother software packages.