High-gain vs Low-gain Headphone Amp

The main difference is the position of the volume knob.
The only person who can decide which is better: low or high output.. is YOU listening to the earphones both ways and YOU deciding: "I like this position better".
That is it.
The theoretical tradeoffs are more dynamic vs lower noise floor. All dependent on the way the volume control responds at different settings.
No one else can decide for you what you would like better.

For MY headamp a Rudistor RPX333mk2 and my headphones, Sennheiser HD800 i like the lower level output better.

THANKS Elizabeth for your opinions and suggestions.
I did follow your suggestions and confer your opinions that I like the Lower level output better with my HD600 on listening to classical musics.You are RIGHT:all I have to do is just to increase the volume control little -by-little to find out "my optimal" sound

It's important to remember that gain and/or volume is kind of complicated. As one example, the AC power coming from the headphone amp will have a certain number of milliwatts. Since a watt always has a ratio of voltage to current (i.e., Amps), two amps with the same gain in terms of Watts may sound very different given the headphones in question and what the ratio between volts to Amps is (1:1, 3:1, 1:3, etc.). By analogy, current is like toque in an automotive engine. So, if you have a pair of headphones that are hard to "get moving", a higher ratio of current to voltage may be required for good sound even if you only have, 500 milliwatts or 1/2 a Watt total. High-current headphone amps include the Cavalli Liquid Gold, the Pass HPA-1, and the Woo WA5-LE. Low current/high voltage amps include, say, the Woo WA6-SE. The best thing to do is just listen closely and not worry about the rest. :--)