I have used both Dragon and Viavoice programs.  I have not kept up with
viavoice but I have with dragon which just came out with version 8. and is
extremely accurate, preferred edition going for about $169., have not
tried the professional edition which is way more expensive but have found
preferred to be sufficient for most purposes.  I had a student who used it
with jaws a couple editions ago, her difficulties were more with her voice
quality reducing accuracy, I do not recall any conflicts with the 2
programs but  I myself do not have any experience using the 2 together.
Probably most important weather using a screen reader or not with voice
recognition is turning the microphone off when not directly dictating.