From the top of my head:
There's basically a few things you'd want to have from a "perfect" amplifier, but which are hard to realize within a single one:
- High Common-Mode rejection ratio (CMRR)
- High Input Impedance
- Low Output Impedance
- High Gain
- Low Noise figure
- Low Output bias
In a three-Opamp differential amplifier (and I'd assume that things like the INA128 actually are made of three opamps!), the input impedance of the output opamp doesn't really matter – so you can use something with a lower input impedance, but with a high output drive strength. In fact, I'd speculate that it might even make sense to use BJTs for the input stage differential amplifier of that third opamp – you'd be sinking exactly what need, and:
That third opamp would ideally have a high CMRR – and it's, I've been told a bit easier to use laser-trimmed on-die resistors to make this thing a little more symmetrical if these resistors are lower value due to more current flowing through them.
So, wild guess: Third opamp input differential stage: BJTs, rest FET, with a relatively fat FET pair at the output.
The two input Opamps wouldn't need as much CMRR (in fact, none, as long as they react identically), but a high input impedance – an ideal use case for FET inputs.
Friis' noise formula tells us that these two mostly define the noise figure of the overall circuit, so it's at least likely the stages after the input stage are also BJTs. A significant amount of the overall voltage gain might happen here (for exactly Friis' noise formula reasons).
I mentioned laser-trimmed resistors: Since you need to really get the resistors in an instrumentation amplifier right, the streaks of weakly doped silicon that make up resistors on ICs are in this case designed to be "zappable" with a laser during production – meaning they can be adjusted after / while being measured by calibrated equipment.
Because I can:
The three opamps for which I could find die shots (which I'm not competent to interpret: