see above chart as an example. a line straight across at 0db would be completely neutral and flat (not realistic!). peaks are areas which are emphasized while valleys are areas which are recessed. bass (low frequency) is on left while treble (high frequency) is on right.
the dt770 peaks a bit less in treble and has more sub-level bass. it also has more significant v-shape and drop in mids. dt990 has a bit less bass and a bit higher peak in treble. dt880 is similar to 990 but is a little more flat and does not peak as much in bass or treble making it a little more neutral sounding.
dt990 will have more bass than the hd598. for open headphones which normally do not have much bass it does fairly well. as far as soundstaging is concerned, not sure if its bigger but its at least equivalent.
can the dt990 be a bit fatiguing? yes. this can be reduced a bit with equalizer and they do lighten up a bit after burn in. the hd598 is almost the exact opposite - it is more mellow and laid back whereas the 990 is more detailed and aggressive. both can be good depending on your preferences. also keep in mind that unless you have music or audio with very high amounts of high frequency treble you may not have much of an issue. the headphones only play what you push through them.
seems pointless to use the mixamp with an amplifier - why wouldnt you just use the one. it can be done however i would have the mixamp on minimum output volume and use the headphone amp volume control as you dont want to be double-amping as there is a reduction in quality (slight). of course you could always test with the mixamp alone first then make up your mind later if you find its not powerful enough and need something else to power headphones. technically any analog input amps should work with the astro.