I haven't done an A-B comparison of the same game, but I've noticed live sports on ESPN channels on PS Vue (via a PS4) have been looking better since I first signed up last June. Sometimes I forget I'm watching a game streaming on Vue as opposed to watching on an OTA network.
Watching games via Watch ESPN from a Windows PC connected to my TV is acceptable only as a last resort. Though in all fairness I'm normally watching games that ESPN deems not worthy of their main channels (ESPN/ESPN2/ESPNU) and therefore may not be broadcast using their best equipment. For example last week, I watched an FCS first round college football playoff game featuring a local team and was just happy I could watch it at all. PQ was actually better than expected for a muddy game at Cal Poly San Luis Obispo.
EDIT: I just had a total Doh! moment, realizing I can now use the Watch ESPN app on the Amazon FireTV stick that's now connected to my living room TV. lol
I just checked out a replay on Watch ESPN (FireTV Stick app) of the Mountain West Championship game I had watched live last night on ESPN via PS Vue on my PS4. The quality of the live broadcast on Vue was noticably better on my 46 inch plasma. Then checking the recording on PS Vue of the same game on the Fire Stick, the quality was only slightly better than on Watch ESPN, but not as good as on my PS4. It's worth pointing out, I've never done any kind of callibration on the Fire Stick's input.