Was going to say F1, but I wonder if that's just my perception based on how rapidly F1 has degraded as opposed to where they actually stand, so I'll try and look at this rationally, although not following NASCAR does make this a bit hard and subject to error:
Championship - F1 has double points, but doesn't NASCAR have a winner takes all finale now?
"Winner": NASCAR.
Lapped Car wavearounds - F1 waves all cars around regardless of position, doesn't NASCAR just wave around those between the pace car and the leader?
"Winner": F1, but may be a tie if my info is incorrect.
Overtaking - Maybe passing is easy in NASCAR, but that's a natural consequence of the cars allowing slipstreaming and so on, it doesn't have DRS as far as I can tell
"Winner": F1
Car Numbers - While similar, at least the permanent numbers in NASCAR are attached to teams rather than drivers
"Winner": F1 narrowly.
Restarts - Since NASCAR doesn't have standing starts at all, I'm going to say their double file restart and F1's standing starts are essentially an equivalent
"Winner": Tie.
Finishes - F1 doesn't have GWC. Yet.
"Winner": NASCAR
Tyres - Both have spec tyres, but as far as I know Goodyear haven't been asked to produce a substandard product in recent seasons for the sake of "the show"
"Winner": F1.
Fake Yellows - NASCAR still takes this by a mile, for all F1's faults with the safety car procedure, I've never been aware of a recurring theme when it has been brought out many times in dubious instances.
"Winner": NASCAR
Technology - F1 has degraded much in recent years on this front, but at least have new engines this year and at least the semblance of an ongoing technical competition.
"Winner": NASCAR
Entries - NASCAR really pisses all over F1 here in this regard and has for a while, at least allowing smaller teams the opportunity of showing up with a legal car and making the field in qualifying (even if some entries are seeded and guaranteed a start, at least no-one is locked out), as opposed to F1's arbitrary entry tenders and full season commitment BS.
"Winner": F1 by a mile
Performance Balancing - This was always NASCAR territory, but with the way F1 froze the engines in 2006 and then allowing upgrades to make them equal I'm tempted to call this a tie, but then at least from a car point of view F1 allows development and while it will ban things, its a few steps away from throwing all F1 cars in a central windtunnel to equalise their performance.
"Winner": NASCAR
Which leaves my final score as:
F1 4 - 5 NASCAR
So NASCAR still "wins" the most-artificial battle for me but only just, although if my info about the wave arounds is incorrect it means the score is 5-3 in "favour" of NASCAR.