Your question is not the easiest to answer as both SDR and Scanner receivers has 'similar' functional sections, but the design and finial application may force one radio to demonstrate more gain/sensitivity than the other.
In the case of the SDR generally you have the most control over the hardware by use of SDR# so you can take the gain to max and enable any preamps that might be in the hardware. In this case you have a good sniffer program to find weak signals. At the risk of overload in the frontend of the hardware and picking up ANY birdies in and around your receiver.
The scanner has a more focused application and while the RF stages might have the gain and sensitive capabilities of the SDR, by design it would be better to limit the gain/sensitive so the scanner only stops on real world signals. Reality is most of what I/we listen to on a scanner is a strong signal not needing a lot of gain.
Considering the apples to oranges comparison I would say the SDR is more sensitive than the scanner, but can be compromised by overload and IM interference that would be counterproductive to scanner operation.
If you mean that you're using the same antenna at the same time with both receivers aka you've got a splitter or Y-type connection somewhere in the antenna cabling/wiring then part of the problem is the moment you split the antenna's feed you cut the signal strength literally in half that's reaching each receiver. As noted in the post above, physical scanners are traditionally sold with the RF gain set to a level at the factory where it's determined to be able to provide the best chance of receiving a signal without overloading the front end - they almost always have an attenuator circuit that can be turned on or off as required in a really strong signal area to prevent that overload, but scanners have never really had a "signal boost" type amplifier circuit in them.
Because of this and knowing that most SDR applications support altering the RF gain across a pretty wide range - most of the "cheap USB TV tuners" we all use nowadays aka RTL-based sticks offer up to 49 dB of gain means that in some situations you'll probably be able to get a good signal with that level of control over the gain as compared to the physical scanner with gain you can't do anything with.
While I'm not absolutely positive, as I mentioned above if you're using a splitter to share one antenna with two receivers at one time that's a 50% signal reduction to each scanner compared to what it would be if one receiver at a time had discrete access to the antenna.
Now it remains to be seen what the situation is so I suspect we'll get an update with that info soon enough.
Thank you both for you're detailed replies. I am not using a splitter, just swapping the antenna between the two devices. I am using a 477MHz 12dBi antenna (https://www.telcoantennas.com.au/site/zcg-scalar-12dbi-477mhz-uhf-base-station-antenna). Even though this antenna is tuned for the UHF CB band here in Australia, it does a good job between 400-500MHz. Using this antenna plus SDR# enables me to hit distant weak digital stations 50-60 kms away but using the same antenna with the TRX-2 those same stations don't even break the squelch on the TRX-2.
While I can't say why you're having the particular issue with the particular system(s) you're trying to monitor I suppose the question I'd ask next would be are you having good/great reception on anything else in that range of frequencies with the TRX-2 itself? There's always the possibility the scanner could literally be "deaf" or defective in some respect for some reason in that range, I don't know but it's a consideration.
I get what you mean by saying that you're not getting enough of a signal to break the squelch on the TRX-2 but have you tried it with the squelch wide open to get anything at all? And are you absolutely certain the built-in attenuator is actually off on the scanner and not enabled?
A modern scanner like a TRX-2 will measure very sensitive on test equipment, probably less than .2uv or better. I've measured some receivers that approach .1uv sensitivity but in actual on air listening you can't tell much difference, so small differences in sensitivity would not explain the problem. In no way would a dongle SDR receiver measure substantially better than a TRX-2 unless the TRX-2 is broken.
Receivers connected to an antenna are a completely different situation where receiver overload can make a very sensitive but lower performing receiver deaf to weak signals compared to a receiver with higher dynamic range and less prone to overload. I see this all the time with two way radios like the Baofeng UV-5R measuring way better sensitivity on test equipment over an older Yaesu hand held, but side by side on a mountain top the Yaesu receives lots of things that don't exist on the Baofeng because the Baofeng is a very cheap overload prone radio.
To get to the bottom of the problem you should measure the absolute sensitivity of both receivers on test equipment to rule out a defective radio. Then repeat the comparison using an external antenna, then use an external fixed attenuator of maybe 10dB or 20dB on each receiver and test again.
If a receiver is getting overloaded and not picking up certain signals, adding enough attenuation to bring it out of overload then comparing to the other receiver with the same amount of attenuation will help identify if that's your problem. Its best to use the same external attenuator on each radio instead of the internal attenuation feature so you are comparing apples to apples.