If I want to vectorise or trace in images that I have sketched, should I use Illustrator and use the pen tool to vectorise it, or use Photoshop and use the brushes to draw it (To imitate pen drawing)?
I can't really tell you which to use, but I can tell you the advantages and disadvantages of each program.
There are many differences between the two, but there's a single fundamental difference that created the need for two separate programs in the first place. Photoshop creates and modifies raster images and Illustrator creates and modifies vector images. That means with raster images you will get to a point of zoom in the image where you will get a hard pixel, but with vector you will always get a clean line. The advantage is that you can increase the size of a vector file to any size, as large or as small as you want it.
On the other hand, Illustrator is fairly limited in terms of the tools at your disposal. Colors are either a solid, a gradient or controlled with a gradient mesh. You really have to know exactly how it should look before getting started in illustrator.
I hope that helps!