It depends on what revision of GTR you go for as to how well they handle on the road, the later versions have suspension revisions that improve their behaviors, the early models up to 2011 (the DBA models) are considered to be the most raw. I have done barely any track work with the GTR, a couple of runway charity days giving high speed runs and a training session at milbrook to better understand how to drive it and that is pretty much it.
The biggest problem for me with the GTR is that it has grip for days so in order for it to excite you need to be going extremely fast, or being extremely stupid (most often both) in order for anything dramatic (fun) to happen. That said I can't see me getting rid of it because £ for £ I am unconvinced that the performance can be beaten.
I had a B8 S5 (manual but no sport diff sadly) and rather enjoyed that but found it nose heavy and the steering vague but it could certainly eat up the miles in splendid comfort, directly prior to that a 450bhp RWD converted one off Skyline R33 GTR that went sideways more than forwards which lead to it's ultimate demise along with two other innocent parked cars.
My partner had a B8 A5 3.0d S-line (manual again) for about 6 years that I think handled better than the S5 in the steering feel department. She changed that for a DB9 about 18 months ago now and we had a little Mini One as a runabout/dog car but it was unsuitable for the long trips she sometimes needs to do for work and I have a new job that dramatically increased my weekly mileage that I didn't want to put onto the GTR (as the second owner I have already put 55k miles on it in the 6 years I have had it)
Thus the requirement for a "sensible" car that would suit the dog better, be properly capable of handling long journeys and at the same time be quick enough to keep me entertained as a daily driver. I had read such good reports on the S4 that I think my expectations were too high and too coloured by the Saloon handling reviews.
All that said it does have a very crap mixed set of tyres on it that need to be changed, I think the strut brace is cheap enough to throw on there and see how much it tightens up the front end (though I do have an idea that involves some carbon tube and machined alloy ends that I think would work well in that role) so I'll do that and see how we go. I can always do the ARB's and see if they do the trick later, they seem easy enough to change over.
If all else fails the S4 was cheap enough to just be relegated to pure runabout/dog car and I've been itching to get my hands on an RS5 for ages so I'll investigate that option.
It would be really interesting to get some views from Avant owners on handling and driving characteristics, it may be that I am just driving it all wrong.