I have been told that the Dyna engine is not a balanced engine?

No they aren't, that's why they have rubber engine mounts. Also why the engine jumps around in the frame at idle, then settles down a bit when up and going.
The softail motors have an inbuilt counter balance set up.
There are pros and cons to both.
But I have been told I am a lunatic.

Well I have been told, from more experienced folk that the unbalanced Dyna motor can be hotted up more than the balanced type ones that the softails sport.
Although this seems a moot point, as I have also heard a well known performance improving identity on this forum say this is not entirely true.
Maybe some real expert will chime in?.

To be honest, once my Dyna is past idle it's as smooth as any HD I've ridden. Maybe I don't notice?

being a new to hd rider i wasnt aware of what was vibes and normal [ '07 fxdl ]. pick up day comes and on the ride home [ test ride around geelong didnt get to highway speeds]the vibes were that bad at around 100 km i couldnt keep my right foot on the peg...got home and checked the front engine mount [after google search] and found the mount had "collapsed",fitted a new mount and the vibes were 98% gone .

its all good jfe hums along nice now.cheers