There are different philosophies for different teams. It is clear that a study of two teams may unearth a great deal of differences in terms of the types of players that they would be looking for over the first two rounds thanks to these schematic differences.
However, over my years of covering the draft and talking to league personnel, I've found that many scouts and coaches have similar ideas of the physical or mental traits that they want from 1st round prospects from position to position. While the prioritizing of these traits may vary, here is a general idea of the most important trait/traits that teams will look for from each position.
Size and Accuracy
Show me a short QB and I'll show you a QB who won't be taken in the first round. The fact that Drew Brees went with the first pick of the 2nd round after playing in a "system" at Purdue is quite shocking given the climate of today's NFL. Teams generally want their early round QBs to be at least 6'2 and to have enough size to them that they can hold up to the hits they will take in playing the position.
Arm strength may excite the general public, but teams want accuracy more than anything. The proliferation of spread offenses and simple, short throws have made it harder to gauge accuracy from college tape, but Senior Bowl practices, the Combine and Pro Day workouts have helped teams get a better feel for those QBs. There are obviously times when athleticism and potential will win out as was the case with Jake Locker going in the first ten picks in 2011.
Overrated Trait: College productivity
Build and Burst
It goes without saying that there is a size dynamic at play for each of the positions that will be listed, but unlike the other positions, height is much less important than weight for RBs. Teams are looking for backs who are well-proportioned and who have the type of build that can take an NFL hit. While different backs carry weight differently, it is safe to say that most teams would prefer their first round backs to be 205 pounds or more.
Tongues wag at the combine over 40 yard dash times, but NFL teams care much less about long speed than they do about bursts of quickness from 5 to 15 yards. The ability to hit top speed quickly can be the difference between turning the corner or getting dragged down for no gain. Similarly, running lanes close down quickly and runners with burst can get through those holes and into the second level as opposed to plodders.
Overrated Trait: Workhorse potential
Height and Hands
Teams have differing philosophies regarding wide receivers. Some teams like the Packers and Saints believe that the QB dictates the success of the passing game and that drafting a wide receiver in the first round might not make much sense from a value standpoint. There are other teams who believe that you strive to find a true #1 WR and then fill-in with talent around them.
Regardless of team philosophy, they all prefer the old, reliable "size/speed" for their top two spots. Granted, not all WRs will fall into the size or the speed category, but that is what teams want in the first round. WRs with height have huge advantages down the field in one on one matchups against smaller CBs. And while it may seem like a given, teams take drops very seriously. An inability to catch the ball consistently or with the right technique is grounds for dropping a prospect by at least a round in some instances.
Overrated Trait: Route-running
Strength and Flexibility
Quick feet are the rage when it comes to amateur evaluators (including those you see on television) and their discussion of offensive tackles, but what too many of them miss is how to properly evaluate and prioritize functional strength. It is one thing to get bull-rushed due to a lack of technique, but it is quite another for a tackle to get consistently walked back into his own backfield because he lacks the functional strength to battle with the player in front of him. Tackles who lack foot quickness can get help in the form of a chipping RB, but tackles who lack strength have to have the entire protection changed too often to help them out.
Offensive tackles are getting taller and taller which means that their centers of gravity are getting higher. Maintaining proper balance is much easier for tackles with good flexibility who can bend and create a slightly lower, more powerful center of gravity. Flexibility is also important as it helps tackles (and guards) coil up and fire out with lower pad level and with more explosion in the running game.
Overrated Trait: Run Blocking