I almost lost hope that I'd find out some electrical information for the hall effect joysticks, but then I found an oasis of information: Metal Plastic Electronics (which I'll abbreviate to MPE). 

It's a channel that has dug for details on many of the electromagnetic joysticks on the market! This log kind of serves as a TL;DW. I'll try and speedrun though the things I learned watching his tests yesterday, starting with a video where he tests these:

The rise/fall time of yellow (Ginfull) sticks are unbalanced

The one I found on ebay are the L4A sticks:

As it turns out, a capacitor is on the output pin meaning that it has to discharge when the signal voltage is lower than it. This results in fast rise times but very slow fall times. In a comment, MPE tried using pulldowns to no avail.

This might not be too noticeable when orbiting around in spacemouse mode, but it's going to lead to overshooting if used as a trackpoint. 

As you can see, the magenta trace is a (not so traditional) potentiometer stick and cyan is Ginfull hall sticks. MPE manually moves both sticks to and fro.

The rise/fall of the blue and green sticks are fast and symmetric

The green sticks use a larger magnet, so it seems they'd be less susceptible to stray magnetic fields than the others. The drawback for this application is that the sticks don't have a cylindrical hole, meaning I can't screw in a ball to the end of it:

The blues/greens are similar in price.

The sticks likely accept 1.6 - 5.5V

The chip inside the Ginfull hall effect sensors is rumoured to be the Hallwee HAL9303, which has the following voltage ratings:

• 1.6V Min
• 3.3V Typ
• 5.5V Max
• 7V Abs Max

MPE used 1.8V in his testing.

TMR sticks use low power to output a signal that closely matches the magnetic field

For example, here are the Hallpi TMR joysticks, which are about 2X the price of the average hall joystick:

There were also the blue K-Silvers (cheapest) and black GuliKit on his channel.

TMR sensors seem to pull around 210uA of current, compared to 700uA for the Ginfull L4B board (which was found to be identical to the L4A board).

Ginfull TMR recently arrived on the market?

So I was thinking that I was going to get the blue joysticks below:

But I also noticed some translucent Ginfull TMR sticks:

I found another listing where the price difference between the two options would be pennies, both effectively being £16 including shipping and VAT. 

If these were like the other Ginfulls, I'd have to skip them. If they were like the other TMR brands, it's an easy win. One of the only references I could find was a 15-day-old post on reddit and 2-week-old comments under the Hallpi video with MPE replying that he had them on order. 

Thus, I went to bed hoping that the video would come out in the near future.

The TMR future is now!

MPE published a video of them today:

They share similar components to earlier hall-stick designs, but they have all the benefits of TMR with none of the filtered output:

The current draw is typically around 215uA, up to 375uA if the chip is outputting VCC (1.8V in his testing). 

[Edit 1] MPE also heard from another commenter that the chips inside the TMR joystick may be the TMR2615x-AAC.