I measured the output from Out Left and Out Right compared to the Headphones output and they are exactly the same when connected to the same stereo input on my sound card.
Using headphones is another story since different headphones are more or less “loud” compared to each other. So if the same master volume setting on the A4 gets to loud or not to when you’re using headphones depends on the headphones and not on the outputs. (Unless by chance your A4 is broken.)
I’ve set my inputs on my sound card to +4dBu, which is standard for connecting equipment like the A4, and I’m getting a very clean and good signal. Other gear, like a Moog Minitaur I used to own, had a lot hotter output but I wouldn’t say that made it sound better, just louder.
What if you raise the level of the A4 in Ableton, perhaps with a compressor (you got the lovely “Glue Compressor” in Ableton right?) just a few db. Does it get it’s punch back or is it still dull sounding to your ears?