I rode two parts of EV6 last year, the longest stretch was from Passau to Vienna. It was mid-July so very definitely peak season and I didn't find it that busy. Yes there were more cyclists and bike tourists than we were used to seeing (having ridden 1700 miles to get there) but it wasn't packed and certainly no bike traffic jams!
The route is wide and fantastically surfaced. Most of the time you are on the riverside path away from roads but there are a couple of stretches either adjacent to busy roads or on quieter roads (the path out of Passau comes to mind as one of the former). Often the path runs on both sides of the river and it would be worth researching in advance which side to be on as there's no useful info on the road which helps you decide.
I loved this part of our tour and it's worth taking your time to explore the places you ride through. Some I recommend:
Passau, a very pretty city
Linz centre (the outside is a bit dull and industrial but the city is worth a visit. We had a couple of issues finding a campsite)
The stretch from Melk to Krems - my favourite day's riding out of 3800 miles.
If you are there in the summer be sure to gorge on the extremely tasty Wachau apricots and perhaps a glass (or bottle) of Gruner Veltliner.
To read more do take a look at our crazyguyblog - http://www.fuelledbycake.co.uk
. This page
has a quick link to all the days we rode EV6 (including Besancon to Stein-am-Rhein).