I'd take NFL 2K3 over any other football game, and I hear ESPN improves it alot more. This is my advice for NFL 2K3, since it's the game ESPN Football continues from.
Anyways, on offense, docbungle gave you the simple-yet-effective advice. In 2K3, I find flag and square-out routes (where a reciever runs straight for afew yards, then cuts towards the side-line) to be the best routes to get open on. Also remember and practice this: there's a BIG difference between a bullet-pass and a rainbow-pass. If you start passing alot to a certain side (and especially if you're successful in doing so), then sneak a Speed Option run-play to the other side of the field to teach their defense a lesson or two.
On defense, it depends on what position you're playing. Assuming you're not trying to blitz in the particular defensive play...
Defensive Backs (Free Safety, Strong Safety, Cornerbacks) - Either stay in your zone or stick with your man, whichever your defense tells you to do. Watch out for the deep pass first and foremost, but when it's obvious it's a run then angle yourself as best as you can to get to the man with the ball.
LineBackers - Either stick to your zone or your man, whichever your defense is meant to do. Generally, they need to watch out for the run and/or the short pass first. Again, once you can tell it's a run you need to angle yourself correctly to get to him. If it's a short pass, try to deflect/intercept it if you can if it's anywhere near you, and run straight for the ball-carrier if it's not. If it's a deep one, naturally, you probably don't need to think that the LineBacker'll be back there, but it never hurts to have them running back there in case there's a fumble that needs recovering.
LineMen - If it's a run up the middle, do your best to block the gap that is most open or the ga it loks like the ball-carrier is running to. If it's a Sweep, break free from the Offensive LineMen A.S.A.P. and try to get to the guy. If it's a pass, do everything you can to either rush the QB or deflect the pass.
...Of course, if it's a blitz, simply blitz into the correct spot and hope for a sack.
Lastly, on Kick-Off, don't go for an Onside Kick when it's raining, ever. The ball'll stick to the ground instead of bouncing, and often-times will be a penalty against you.