What are the important specs to look after for IGBT replacement?
The internal diode won't matter if the circuit has external diodes.
Never operate a IGBT at more than it's maximum gate-emitter voltage or collector-emitter voltage or it will blow. These two ratings are the most absolute and the easiest to understand.
Collector-emitter Saturation voltage is next important and determines the voltage across the IGBT when conducting which determines heating. Similar to source-drain on resistance for MOSFETs,
Make sure to compare saturation voltage at similar applied gate-emitter voltages. Note the gate-charge vs Vge curve is much better than the number listed in the table.
All specs, especially timings, are subject to the test conditions. So you can't directly compare them between datasheets unless the tests conditions are the same (and they won't be a lot of the time for timing). Test conditions are usually listed in the columns right next to the specification. I basically ignore any specification given in seconds. They're kind of useless.
Gate charge and capacitance determine the timings and are more important than timings given. Note these are also measured under different conditions but these tend to be a lot more comparable than timings. Between charge and capacitance, I ignore capacitance if charge is available as it tends to be more directly comparable.
Higher gate-emitter charge/capacitance leads to longer timings and can lead to overheating while the IGBT is busy switching due to spending too much time in the inefficient (i.e. high loss) region between fully conducting and fully blocking, so try and not stray too high above here.
But lower gate-emitter charge can cause switching to be too fast which is efficient (less heat) but can result in reflections and ringing which can result in voltages that can blow stuff if the design is really border line.
For capacitances other than gate-emitter, higher can allow parasitic currents to flow and cause latching or other problems so smaller tends to be better for these.
All things being equal, you cannot go too low with saturation voltage, too high with gate-emitter or collector-eitter breakdown voltage, or too low with charge/capacitances OTHER than gate-emitter.