Bring back the old days I say. let the teams make their own decisions as regards tyres, fuelling etc. Then truly, the best team wins. I do agree with putting a cap on budgets though. Some teams just arn't as well off.
On a contraversial note, F1 could adopt the same as golf. have handycaps and situate teams around the track as they see fit. To do that would mean either let them go early and do the same amount of laps, or they start at the same time, but do less laps. You would see the front runners really pushing then if they need to reel in a couple of laps on the slower cars to be able to finish in any kind of position.
The handycapped teams though would not necessarily get the same reward money as the better teams, but that could be used as an incentive to catch up.