There is no winner! While I've done my best to metaphorically create a competitive fight between the two programs, the bottom line is it all depends on what you're trying to create and how you work.

Having a solid understanding of both Photoshop and Illustrator is essential for most designers, whether a web designer, graphic designer, fashion designer, illustrator or any other type of digital creative. Knowing these programs well is going to ensure you choose the best program for the task and create the best possible output.

Many designers will have a preference over which program they prefer to use but that should never come in the way of producing the best possible creation, whether in regards to usability or aesthetics. What is the most important is that you make it your responsibility as a designer to know BOTH programs and know them well.