I have used Dragon on and off years, and as we have had an influx of potential clients who are not skilled typists (or interested in learning to be), we talked with other Docs who use and recommend DNS-Medical, and ended up establishing a business relationship wit h Dragon. [Disclosure]
As far as faster - what I have observed is that it seems faster, but I'll let other speak of their first-hand experiences.
As far as cost justification, I have done a few of those for the board over the years. So, using numbers provided by others, I would estimate that over a year, you would have to be able to save between 1-1.25 hours per month to re-coup your initial cost. If you choose to spread the cost of the software over 3 years and didn't choose any additional support or upgrading, that means you need to save between 20-30 minutes a month.
Having been dependent on
sleep spell-checkers for years, I am glad to have a medical professional confirm that is is all because I am left-handed.

And spell-checkers don't fix everything as evidenced.