I first ran 28 off in October 2014 so that's 8+ years of being able to run that pass. Only in the past year can I say I can run 32 with any consistency at all. Because of that, I'd say I've got a pretty fresh perspective on the difference between these two passes.
The difference is difficult to see for most coaches and difficult to understand for anyone who has been running 32 and shorter for a long time, or for most of their lives. Because of that the wrong advice is given most of the time by most people. Most people are coaching things that are a visible result of a largely invisible problem. Credit to @scoke for noticing this with my skiing.
You can't easily "see" line tension from the boat or "tell" how hard someone is pulling, but this is the issue that gets you at 32. You can "pull" at 28, and you cannot "pull" at 32. Oh, you might run an occasional scrappy 32 when you're pulling, but it'll be an event when it happens vs. an expected result.
People that have run short line for a long time "generally" have no idea how much longer-line skiers habitually pull vs. "lean and hold". You can't really see it when coaching but it prevents, most importantly, all pre-turn technique from occurring correctly, and resultant position out of the buoy as well. You can't get hips up, be tall, be level, be patient, or anything like that from spray to ball if you take rope tension behind the boat.
You can pull all you want and still run 28, so if you are struggling with green, STOP PULLING. Stop denying that you are pulling, too. Take a comically, ridiculously less amount of tension through the gate and wake to wake. Ski with the ski and not the handle/rope. You likely have NO IDEA how LITTLE rope tension there should be behind the boat. When I figured this out, I started seeing it everywhere. Good skiers who ski big buoy counts stay still behind the boat and don't take barely anything through the line wake to wake. They finish the turn and hold. This "allows" any chance at doing anything correctly before or after the buoy.
FWIW, YMMV. I'm still working on this every set but I'd say it's the most important thing.