What pros and cons do the diff pictured have over/under the common bevel gear type of diff?

Really no difference as far as both the bevel gear and straight cut gear versions are open differentials. They have just taken the bevel gears and replaced them with straight cut gears.

One pro of this design is with a bevel you must closely control the axial clearance so that the bevel is neither too loose or worse too tight. With straight cut gears it's easier to control the gear backlash.

The other pro I can think of is with the straight cut gears there is no thrust caused by bevel gears transmitting power. With bevel gears they try to wedge apart so ideally you need a bearing that can take thrust load, or with a typical design they just use a thrust washer, thus creating a little drag. So with the straight cut design I would think there would be less drag.

I also notice that instead of 4 spider gears like in most diffs, this one has 5 spider gears. It should make this diff a little stronger but I could see that it might be more sensitive to diff oil viscosity changes because there should be more viscous drag using 5 spiders. But overall, I doubt you will see any significant differences.

NOTE: The spider gears only move when one wheel is running faster than the other side (going around a corner).

It looks interesting, as far as i know only the Tamiya Avante has used these planetary differentials before(?) but that thing was terrible.

I'm really curious about these truely having less drag, and if they do whether it's noticeable in any meaningful way.
They only start working when you're cornering and presumably also braking or slowing down, so having less drag in the drive line at that moment seems negligible.

Perhaps in long fast corners you'd have small gains?

Corally had one far in the past

Team Corally SGX Spur Gear Differential

Traxxas has been using planetary diffs forever.

Excelerate has their new 1/12 scale straight cut gear diff too.

https://exceleraterc.com/prodigy-gear-diff/

The diff is meant to have drag, that's why we put viscous oil in them.

Never even considered that, so no real benefits then..

More gears = more teeth = more drag

All 8th scalers used straight cut gear diffs until the mid 80's and they all went to bevel gears then... That tech was abandoned litterally decades ago. Not exactly sure what has changed in the hobby lately that could explain how they'd return to form other than the novelty effect.

I noticed that too, my first 1/8 buggy had those. I found that no matter how thick the silicone oil was, it got flung to the outside of the diff and provided very little diff-action. My next buggy had bevel gear and it had so much better power delivery though the turns.