No question!! YES!!! with paint the pigments are better and paper holds both water and paint differently
Inexpensive student grade watercolors from Reeves on Canson XL Series 140 lb cold press watercolor paper
M Graham watercolors on Canson XL Series 140 lb cold press watercolor paper
M Graham watercolors on Arches 140 lb cold press watercolor paper
Conclusion - buy absolutely the best materials that you can afford. Inexpensive papers are okay for learning and trying new techniques, but buy the good stuff to use when you really want to produce quality.
Stay away from the student grade paints for anything except playing and even some student grade paints are been than others, ie W&N Cotman paints are much better that the Reeves paint.
If you are lucky enough to have friends who will provide you will samples of different types of paints, like I did, you can try out several to determine what you like and what works best for you.