When I first rode my Fox 36 Van after a 130mm Float 32 I remember oversteering a few times. The fork was much less "twangy" through rough stuff. So, IMH(unble)O, yes, it makes a difference.
This is the sort of comparison I see a lot on this subject, and its just not a comparison at all, 36's and float 32's are completely different forks and built for completely different things, the difference between a float32 QR and Float32 20mm axle is a direct comparison.. 36 QR would be noticeably stiffer over float 32QR.
I guess not many of us are in a position to know how much stiffer a like for like fork is between QR and 20mm the change usually comes as part of a much bigger upgrade in fork quality/price, better wheel build etc, so of course you new forks are going to feel loads better.
Yes 20mm axle is stiffer… noticeable over a QR debateable, especialy given the flex in wheels and the great big squishy rubber thing around em.