The intensity of Primary is more of direct application. The material you are learning are building blocks that you are going to use throughout your Naval career as a pilot. Introduction to NATOPs (the systems and procedures book on the aircraft you are going to fly), systems, weather, FRR and the rest. Each phase of training, or when you get to fly a new aircraft will send you through another ground school where you get to go over each aircraft's systems. For example, on my road to flying the P3, I went through ground school in Primary for the T34, then in Advanced I went through ground school for the T44, and finally at the FRS, ground school for the P3. Each in its way was more challenging than the previous. But the familiarty with NATOPs and studying techniques I had developed along the way prepared me.
Throughout Primary you will have different tests, and periods of ground school instruction. When you go to Intermediate, they had a week long Instrument Ground School (though it has been a long time since I was there, and this may have changed).
The main thing is, is that the material you are learning is NOT memorize and dump. You HAVE to take it with you, whether it is a procedure (Flop, chop, check, drop or Turn, Climb, Clean, Check, Determine, Deliver) in the T34 or the appropiate systems knowledge to go along with it. There are boundless acronyms and assorted gouge out there to help you, plus talking to your peers. You will study the material in ground school, if you are smart you will go to a static display plane and pracap it, and then of course you will get tested on it in groundschool. From there, during CBTs and then on the flights, you will be quizzed on your knowledge in the briefs before each event, god help you if are not prepared. Then the most challenging part, remembering everything in the plane, whether it is getting from point A to point B for course rules, proper freqs to talk on the radio, of course WHAT TO SAY on the radio and in the correct format, implementing a procedure correctly whether it is the level speed change or power off stall (was that power setting 300 or 400?!?!?), and of course the random questions that the IP may through your way while flying to see if you remember your stuff and how task saturated you are.
So, as you can see, Primary is a much bigger step up in "intensity" than API... I am sure others have differing views.