Ian and Alun are both correct and, by adding their contributions together, you reach yet another significant conclusion...
As Ian says increasing the output gives a greater range of useable aperture settings (allowing you a greater set of options in depth of field).
And, as Alun says, softness is created by diffusion (or reflection). Diffusion means spreading the output of your light over a greater surface area (hence the sheet of perspex or softbox or umbrella).
Unfortunately, diffusion absorbs power. If you use a diffuser, you'll need much more power to achieve the same aperture than you would with a bare, non-diffused, flash head.
So, if you want soft lighting for portraits, say, you'll probably need more power - especially if you want lots of depth of field at the same time.