Everything has stronger bass
at higher loudness. Did you level match the amplifiers ?
Other than that, it is actually quite possible for onboard headphone outputs to have audible issues with bass response, and it is not because of lack of power. They often have rather high output impedance (the Realtek datasheets recommend up to 75 ohms external resistors for some codec chips), although that is more likely to increase bass levels with full size headphones, at the expense of somewhat increased distortion. The outputs are also frequently capacitor coupled, with the datasheets suggesting 100 uF capacitors for the headphone jack, and 4.7-10 uF for the line output. Too small output capacitors cause audible bass roll-off, for example 100 uF combined with a 100 ohms load attenuates 16 Hz by 3 dB. If you actually used a line input to drive headphones, then it is obviously much worse, and the line output also might not be able to supply enough current to drive the headphones at a sufficiently high level without audible distortion.