Randy hit the nail on the head. There are actually two factors at work.
1) Jetlag - caused by moving across timezones
2) Travel fatigue - caused by traveling, even within the same timezone (i.e., north-south)
Both affect different people to varying degrees. The worst I ever had was actually a redeye flight Seattle - Orlando. We went to Perkins which offered a bottomless pot of coffee, and I think with 3 coffee drinkers, we went through 3 or 4 large carafes of coffee and still barely stayed awake!
My trips to Italy, I was generally better off. Like Steve, I try to sleep on the plane and sun and fresh air seems to be the best cure for me. My first trip, I landed at 7am and once I got to the hotel I ditched my bags and went for a really long walk. Around 1pm or so, I passed out cold for a 2 hour nap. I did ok the rest of the trip but had a hard time sleeping through the night and ended up relying on Tylenol PM to knock me out a few times.
Second trip, we landed around 1pm and did kind of the same thing--dropped the bags at the hotel and immediately went out sightseeing. We did casual things that didn't require reservations or brain power, such as visiting Trevi Fountain & the Pantheon. Went to dinner after our walk and then returned to the hotel around 10pm and crashed in bed about 11. Had pretty much no difficulties with adjusting to the time shift after that, so I think the later flight helped.
Overall, in my experience what you do prior to the trip--other than not stressing yourself out--is not going to have as much impact as what you do when you first arrive in Europe.