I was looking for a description of what kind of style these images are:
How can I replicate this style and also would I be better use Photoshop or Illustrator for it?
Nowadays, you can use either tool to accomplish these types of graphics. Adobe Illustrator is primarily a vector-based program, it has some raster-only elements available, such as drop shadows or outer glows. Likewise, Adobe Photoshop now allows you to work with vector-based objects (called smart objects) within the traditionally raster-based program.
It all boils down to the tool you're more comfortable with. I personally am more comfortable with Illustrator and would use it for this type of graphic.