I don't own this DAC/headmap, but I like it, hence following this thread. My below thoughts are purely based on it's specs and no real measurements or even listening, so feel free to take this with a grain of salt.
Balanced (XLR3/XLR4): 300 mW + 300 mW (32 ohms), based on manufacturer's specs:
https://www.pioneer-audiovisual.eu/sites/default/files/datasheets/english/U-05.pdf; also
1st post from this thread says exactly the same thing. That means around 3.1V RMS @32Ohms cans; most likely for 600Ohms cans the output voltage will increase a bit, but not much, so I will give you a rough estimation of 3.5V RMS which means about
20mW @600Ohms.
Based on
Tyll's wrote, DT880/600 needs
0.43 mW to get to 90 dB SPL, that means
for 100 dB SPL we need 4.3 mW and for
110 dB SPL we need 43 mW, so I find 20 mW less than desirable for
Beyerdinamic DT880- 600Ohms. Manufacturer states that 100 mW would be the max. power handled, so an amp able to get this amount of power would be recommended, that would be >7V RMS voltage @600Ohms. Don't get me wrong, I don't want anyone to get into hearing problems, but the 20 mW @600Ohms of the U-05 could probably get about 105dB on 600Ohms cans and only if 0dB sinewaves are used; with regular music the average output power will be about -10dB lower.
Just my 2 cents: an amp will pair well with a headphone when peaks of musics will get your cans to about 110dB of loudness with very low THD; that means an average power for the entire track of about 85-95dB, depending on the compression. Not saying we need to listed very loud, but an amp should have enough power reserve when driving headphones, especially for music having a higher dynamic, but also to be sure the output stage if not struggling to handle the output power.
Despite U-05 can drive planars and many "not-easy to drive" 32-Ohms cans, until someone with this combo can actually do some measurements or test, I honestly can't recommend you to pair U-05 with DT880 600Ohms.
Also, some measurements here, but not on the headamp itself:
http://www.audiovideohd.fr/tests/431-Pioneer-U05-0.html.
P.S.: My Objective2 headamp has a max. output voltage of 3V RMS for low-gain and 7.3V RMS on high-gain and I always use the high-gain when listening to the music. I do the same for AKG K701, too, but all of my other can can be very well driven from the low-gain, so it's all about headphone impedance and their sensitivity too.