As far as I know, nobody has yet reported any careful listening comparisons - so the best I can do is to identify the technical effects. The main technical difference will be the damping, especially the effect on bass tuning.
The Jäger was designed and voiced for SETs with no feedback, which have a modest damping factor of about 3. The Aegir damping factor is specified as ">100" which is typical of high-feedback solid-state designs, so it will probably sound a little different. It's not a lot, maybe a one or two dB increase around the 3kHz crossover and similar disruptions in the deep bass.
You can correct this by using a resistor in series with the speaker - I'd recommend around 2.7 ohms, though experimenting with different values would be a good idea. This won't make it sound like an SET, but it will correct the tuning.
(If you play it loud, that resistor can get hot, so it should be a wirewound power resistor, conservatively rated for the same power as the amp.)