I don't want to portray myself as an expert, nor particularly experienced. But I've been round this block before in the past myself. There've been several times when I've plugged in an external amp and thought, "Wow, the headphones certainly sound better, the bass is definitely tighter." ... only to realise that of course it sounded better, it was louder! As Jane Austen wrote, "It is a truth universally acknowledged, that music sounds better when it's loud." So the question really becomes, 'How loud do you want it to go?' and there are clear and easy ways to work out if an amp (or the output stage of a DAP) can do what you want, as long as you can track down the right numbers. The real problem is that manufacturers are shying away from releasing proper specs for their devices these days since they don't see a marketing advantage in them, so we have to rely on independent reviewers who have the equipment needed to test this stuff properly.
A modern amp really shouldn't change the tone of the music in any noticeable way. Of course that doesn't mean that it can't: the frequency response might be skewed outright; the output impedance might be too high, meaning it interacts with the reactance of the headphones and alters their tonality; or it might be some exotic design like a tube amp that has voltage sag and compression in the bass. But the vast majority of modern solid-state amps are all very well behaved when run within their design parameters ... and all sound the same as a result, as they should. You just have to work out what are the parameters you need (power output into a specified load and output impedance) and then find one that matches those.
But if you do go comparing DAPs and amps, make sure the levels are matched reasonably well. It's sometimes tricky to do this by ear, but you could do this with a sound meter on your phone, just jam the earphone against your phone's mic (make sure it's in the same position each time) and play a test track, this should be good enough for a fair comparison.
