It's difficult to generalize intake design principles, since the majority of the intake's design will be largely dependent on the game objects for the year. There are, however, two general principles that tend to identify the best intakes - the intake must be the fastest subsystem on the robot, and the intake must allow the driver a lot of room for error.
The need for a fast intake is best seen with top roller intakes for intaking balls, such as in Nothing But Net or Toss Up. The intake speed must always be faster than the drivetrain speed, otherwise the robot will push balls away as it drives towards them. In general, most robots perform best when they can intake and drive (at least at a somewhat moderate speed) at the same time, so the intake speed can limit the usable speed of your drivetrain if you're not careful.
This principle was the guiding factor behind claw use in Starstruck. Sure, claws had a large capacity compared to other intakes (with the notable exception of 2188A's massive claw: https://www.youtube.com/watch?v=h7fEumWSP9A), but the major selling point on claws was the ease of driving. 2188A's claw was difficult to drive with and couldn't grab objects like a claw could, whereas Aura's The Fat Controller (https://www.youtube.com/watch?v=DaxG2CapSvs) could navigate the field with relative ease despite its massive reach. 2188A's claw did well at skills, where it could be slow and was controlled autonomously, but Aura's claw won worlds.