Illustrator is great for making vector art, meaning not only does the quality of the work not go down no matter how big or small you make it, but it also gives you greater control over the shapes you make once they are complete, at least compared to Photoshop (I love the pentool in Illustrator way more compared to the one in Photoshop, because I feel it gives me way more control over the shape I'm making).

The problem is that everything, from shadows to reflections, must be done by hand. Theoretically you can add shadows like you do in Photoshop, using effects that come with the software itself, but they are not nearly as good as they are in Photoshop and can significantly slow down Illustrator.

The only reason I use Illustrator is that I don't know how to draw, and even if I did, I don't have a tablet, therefore it is much easier to make this type of work in Illustrator when you lack skills or equipment than it is to do the same work in Photoshop.

I guess they both have their own advantages and disadvantages, but unless I really need vector work, or unless I have a project in mind that can only be done in Illustrator, I will always choose Photoshop.

As for the texture added in Photoshop... I don't know, honestly. Obviously you can do that, but unless you know exactly how to do it, I think you can easily ruin the illustration you made, simply because in Illustrator things get to have a certain... style, that differs from Photoshop quite a lot.

In the end, the person using the software is the one dictating the quality of the resulted work. Someone who knows Illustrator very well can make incredible artwork and knows exactly what can and can't be done with the software. I'm not good at Illustrator at all, so most of the things I say are based on my own limited experience.