I made a post regarding onboard audio in gaming mobos here: Demystifying onboard audio
The bottom line is that your mobo is capable of driving those two headphones with ease, but there are some caveats.
The DAC in your mobo is pretty decent as long as it is properly shielded, which normally they are in modern mobos.
The problem with onboard audio is the output impedance of the AMP is too high, funny enough this changes the tonality of low impedance headphones the most. There is a video explaining that in the post.
I also have the SHP9500 along with a DT880 Edition 250 ohm. There is an audible and measurable difference in my SHPs when I connect them to an external DAC/AMP with a low output impedance. That means the output impedance changes the tonality of your cans, so most likely you are EQing something that has already been “EQed” by the output impedance of your integrated AMP in the mobo.
Does it matter for gaming? I don’t think so. Does it matter for music and critical listening? yes.