Attached is some frequency characterization for the Hall sensor. And although you don't seem to be having a problem with the higher frequencies, I also did the coil up to 1MHz since I already had the sweep set up.
The Hall sensor was supplied by +/-5V with each leg in series with a 220R resistor, as previously described by user vtp. I also confirmed I have the 220R resistors on both my probes. The output voltage was measured differentially across the two outputs. The outputs have an offset above ground of about +236mV, and between them about 4.7mV. No load was placed on the output except the probing. A test of a 1k load did not affect the output significantly, so it seems the Hall output is a fairly low impedance.
Likewise, the coil output was measured differentially across its two outputs, but because it's floating it won't matter if you do it single ended. The coil output was loaded with a 50R resistor. I don't know if that's the actual impedance seen by the coil, but at least it will serve as a basis for comparison.
The signal generator was set to 16Vpp with offset 0V. One leg of the output was looped through the probe transformer halves and terminated in a 50R load.
I don't have a Bode plot on my scope, and I didn't feel like writing one. So, what you see horizontally is a full sweep at the noted start and stop frequencies, and then a closer look at the start, stop, and 3dB point. The scope has an RMS ratio function between two traces, so it was easy to find the 3dB point by spinning the horizontal delay until the ratio was down 3dB from the maximum. The sweeps include 20kHz, which is where you were having the most severe drop-off.
The DC response of the Hall sensor was 44.4mV/A, measured at 1A.
Hopefully this info will help you evaluate your Hall sensor.
One thing you should check, if you haven't already, is that your TekProbe interface has all the +/-12V and +/-5V supplies working. You could also verify the Hall +/-2V supply at the head. But given the lower impedance of your sensor, it's probably going to be low.
Also make sure the Hall and coil are isolated from the sensor's metal shell.
EDIT#2: Ever have one of those days? I discovered my connection to the 50R load was bad throughout the AC measurements. I've removed all the previous screen shots and re-posted updated full sweeps for the Hall and coil, both 100Hz to 100kHz. I didn't mention it before, but it should be obvious the frequency on the X-axis is logarithmic.
I'll just tell you the numbers derived instead of posting all those detailed screen shots again:
Frequency at reduced signal
level from maximum (Hz)
-3dB -6dB -10dB
------ ------ ------
Hall 2.3k 4.0k 8.1k
Coil 2.3k 1.3k 775
Hall @ 100kHz = -21dB
Coil @ 100 Hz = -24dB
The sweep envelopes now look right and the numbers make a lot more sense.