Highly recommend the 636, I have an 06 model track bike, the thing tips in great! Get the suspension set correctly to suit your weight and riding style. Great fun out on the track, makes big lean angles feel effortless
I don't have any complaints with mine; the build quality is far and above my 7R, and it's given me zero problems in the year I've had it. Easy to work on; thus things to look for are the usual you'd look for on any bike...
However I think if you're tracking I feel there are better choices, namely the R6 or 675.. My (limited) experience is similar to yours in that I find the handling on both of these bikes more precise than the 636..