Don't listen to them. Studies have shown that the human brain compensates for any loss of reaction time due to aging by applying experience in it's place. I'm old as shit and my K/D ratio is in the top 75% on COD because I out think people while playing.
So now you shoot people in the back? :p
I'm 43 now, lost interest in competitive fps a long time ago so not sure how my reaction times would be, probably not good. I used to kill it at Half life death match and Unreal tournament in my early twenties, then never really got used to a controller for fps.
Racing is still fine, yet that's not so much reaction time as planning ahead. Although perhaps that is why the AI had so much luck spinning me out :/
Anyway as others have said, check display lag. (If you have trackmania turbo, there is a test mode in there that will show you the input lag by letting you press a button 5 times from a screen prompt) Connect direct to tv (amplifiers add lag), game mode, no fluff enabled.
Sit closer, less travel time fot the light to reach you. Jk, but the bigger fov helps with aiming.
Check your ping time. Does Overwatch use a server? What is you ping time to the server location? If it's peer to peer, perhaps you used to be the host in CoD, yet now Overwatch favors others?
Ive got an LG plasma tv and i play Overwatch on PS4 not pc. How do i check for this lag you speak of