There is a difference. In general, waterbased will have less or no hand. White waterbased ink does have a hand, but not as much as plastisol. The rest of the inks generally have none, especially after washing. You can eliminate the hand of the whites by discharging if the shirts are dischargeable.
You also need to use an emulsion that is water-resistant, or the stencil will break down.
Waterbased inks do require you to move along and keep the screen flooded between prints as you work, and a quick cleanup when done. The advantage of plastisol is it is more forgiving as far as a more relaxed print environment, cleaning up whenever you feel like it.
One thing that contributes a lot to the hand of the print in plastisol is the mesh count of the screen you're using. If you're printing through an 86 or a 110, you're going to feel dark ink on lights a lot more than if you print the same ink through a 230. A print/flash/print of white through a 156 will feel a lot softer than the same through a 110 or coarser. Different brands of ink print differently, in terms of smoothness, and your technique makes a difference. Do a search on these forums for something like "rough white print" or "rough feel" and see what comes up. White ink gives everyone the most trouble, and it's always the first thing newbies want to try.