Well he probably won't want to have a chat with me, so I'll discuss it with myself if you don't want to participate and see what I can figure out. Maybe someone else will join in the discussion too. There's definitely some very different trunk and leg stabilization function between the two. The "more weight on the bar" advantage goes to the kneeling variant, and it probably also comes in slightly ahead when it comes to mimicry of the movement being accessoried (accessorized? Is it wearing earrings? I'll stick with accessoried, spell check be damned). Since we don't know the OP's program or level of training advancement, it's kind of a moot issue, but still worth thinking about.
I can tell you that the Z Press is great for trunk (core) strength. I consider the Z Press an assistance exercise.
This link pretty much describes the benefits. 8 Reasons Why The Z Press Is My Favorite Pressing Variation of all Time - Fit World Blog
I'll be trying both this Sunday... I'll report what I learn for what its worth.
I'm wondering if the butt on floor is so your glutes and hams are stretched... or if it was because he didn't have a bench...
Any modular spotter arms at your gym? For example, Rogue power racks might not be quite tall enough for a tall lifter to press IN. But their modular spotter arms, that attach to their stand alone squat racks or rigs, might could be put into the pins OUTSIDE the power rack.
At least that's how I've seen most people do pin presses, on youtube (like Alan Thrall).
hammer_strength_hd_elite_power_rack.jpg
My gym uses these hammer strength power racks.
They have the 'step-up' attachments and an antler-esque pullup attachment (with a 200 lbs weight limit... so basically useless any of my purposes).