DT990s can go pretty loud out of a Fiio E11 with modern music (yes, 50% probably). If you usually listen to audiophile recordings with high dynamic range, you could find yourself cranking up the volume (90% or even more depending on the recording)
That said, as you might guess, loud just means loud, not necessarily clear or full sounding. In my experience, even my Fiio E07K (or E10) (USB DAC/Amp) fail to show the full potential of DT990s.
By comparison, when plugged into the headphone out of my Yamaha A-S500, they sound noticeably more open and realistic. This is quite a controversial topic, I'm just talking of my own personal experience (and using well recorded music).
Talking subjectively, using DT990s with Fiio Amp you get the sound of good headphones, and when you raise the volume you start feeling uncomfortable.
On the other hand, when plugged into the A-S500 and raising the volume, the room is somewhat filled with sound, loud and big but harmless. The overall experience is definitely closer to listening to the same track with nice speakers in a proper room.
Comparing the price of a high quality amp with the price of DT990s (Pro version) is not fair, I think. DT990s are great contenders under 400 dollars, that you can find at 150 if you don't mind getting the Pro instead of the Premium version. Price doesn't mean so much this days.
You could drive DT990s with a Fiio E11, and they'll sound good and also loud most of the times, but I guess you won't regret buying a better amp in the future to pair with your 990s. (Something like O2 Amp or Schiit Magni should do the trick I guess - I couldn't tried them yet, but I've read good things about them)