First, the traditional rule--stitch on Aida using a hoop and stitch on linen "in the hand". In actual practice, people do whatever works best for them. Most who like their fabric taut do tend to avoid hoops in favour of scroll bars or Q-Snaps when working on linen or other evenweaves, as hoops may damage the fabric or leave marks. See section "30.2 Hoops, Scroll Bars and Such" for more information on the equipment itself. See section "18. Stitching On Linens and Other Evenweaves" for a more detailed explanation stitching on linen.
Some people find it easier to control the tension of their thread with one method, some find it easier with the other. The most important thing to remember is to use what works best for you.
For the purpose of this discussion, let's use the word "bars" to refer to all those things which can be used to hold the fabric taut--hoops, stretcher bars, scroll bars and Q-Snaps.
Advantages of "in the hand":
Stitching can be done with the sewing method, which requires less motion on the part of the stitcher than the stab method. The sewing method can be much faster.
There are no worries about squashing existing stitches or leaving hoop marks.
The project is much easier to transport without the weight and bulk of bars.
Some people like the feel of the fabric in their hand. It's part of the enjoyment of stitching.
Advantages of bars:
They can keep the fabric taut, for those who prefer this. They can be used with the fabric loose, for those who like the sewing method.
More of the fabric is immediately visible than if it were draped over a hand.
Most bars can be used with lap stands or floor stands. The stands allow "two handed stitching", where one hand is kept above and one hand below the project. Good quality stands are like fine furniture, and keep the current project on display.
People who have trouble holding projects for long periods of time also may find stands useful--they help avoid or reduce effects from tendonitis, arthritis and cramping.