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?
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Both styles, while slightly different, can be summed up as flat vector illustration
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.
you can use both Photoshop as well as illustrator to draw this object but in Photoshop its some how difficult to arrange some vectors. so i suggest to use Illustrator for this object.