Amps do a lot of different things for different people and it all depends on the type of amps we are talking about.
Generally they do:
1. more volume on harder-to-drive phones.
2. kinda goes together with the first one, but: more power to drive the phones. (brings out potential, better control, more energy, etc)
3. add some sort of coloration/EQing to the sound sig. (e.g. boost bass, add warmth, etc)
4. these are done with or without bypassing DAP's crappy internal amp.
So for example, people who prefer RE0's detail but dislikes the analytical sound may use an amp to add a bit more bass and warmth to the sound.
And yes TF10 and RE0 are completely different so you definitely will notice a difference, big difference.
But please for goodness' sake get the TF10s when they go back on sale for ~$90 on amazon and save yourself $90.