First corner at Daytona is definetly a gradual braking corner because it requires trail braking, trail braking corners are normally ones which start with a fairly low curvature and tighten to a sharper corner later on in the same bend. Daytona road 1st corner (or it can be considered turns 1 and 2 depending on how you look at it) is a perfect example, the reason you brake gradually and not hard is because it steadily tightens, the essentially you will only be able to go so fast through the last part of the corner, lets take 40mph as an example of the max speed you can carry through the final part of the corner (the tightest and slowest part of the first corner) if you took the whole first corner at 40mph (its a very long corner) you would loads and loads of time because the first part of the corner is very wide and is also has little curvature, therefore you can go through the first part of the corner at much more than 40mph and gradually slow the car down as the corner gradually tightens, there is more to why the braking is gradual as well.
Even with abs the maximum you can't turn as effectively while braking, there becomes a trade off, the harder you brake the less you can turn but the quicker you can slow down. It works the other way of course, the softer the you brake the more you can turn but without slowing down as much. Thinking of it like this you want to slow yourself down as much in a straight line because you wont be able to turn much if your braking hard in a corner and the result will be massive understeer off the road, but think of Daytona road 1st corner (trail braking corner) you don't want to slow yourself down on the straight becasue the first part of the 1st corner is fast and long so braking down on the straight will loose you lots of time around the corner, but you can't exactly fly through the second part of the first corner at 150mph either, so what to do. Well slow yourself down in the corner of course, but as said earlier if you try and leave your braking to the last second during the corner you will just get massive understeer and go straight instead of turning, what you need to do is brake gradually so that you still get enough turn but are also slowing your car down suffeciently to be able to take the last part of the corner effectively. The more you practice it the better you will become at judging exactly how much brake/turn is required at each part of the corner, but you will have to make minor adjustments to compensate for the narrowing track and tightening curvature, a good driver willl make the transition between braking and truning look fluid rather than hard and agressive, that said other corners need aggresive turning and braking so its all about learning which approach to take for each corner/string of corners, but I would personally say that most corners are suited to the smooth fluid approach than the aggresive approach.
Hope this is helpful
