HDMI will almost certainly provide higher quality sound than the headphone output.
HDMI is passing a digital signal to your receiver, whereas a headphone output is sending an amplified analog signal that probably has a lot of noise. (notebook audio outputs are generally not very high quality)
Something you may wish to see is if your notebook offers toslink/coax out via the headphone jack and a 3.5mm adapter. Toslink would give you galvanic isolation and prevent any possible grounding issues. (common with computer sources)
I'm always grateful for answers, even when they arrive almost six months after I asked the question
As it happens, my laptop has not yet played a serious role in the storage or playback of my music files at home but such a opportunity might arise next year when I make my annual talk to a classical music society (I am hoping to avoid the need to keep loading and unloading CDs by having my selected tracks stored on the laptop). The specs for my laptop say nothing about a toslink option, so I think I just have a standard headphone mini-jack output. That leaves me the choice of HDMI or USB and comments elsewhere have led me to believe that USB is less likely to have any resolution or format limits for stereo or multi-channel audio.
However, this might prove to be an academic discussion. The music society has an Oppo BDP-95, which I strongly suspect has no way of offering gapless playback for FLAC files, something that is vital for a lot of classical music. Unless I choose to uproot my own BDP-105 and take it with me on the evening of my talk I may be forced to continue using CDs. The Oppo BDP-105 has an asynch USB DAC input that supports gapless as long as the source also supports gapless (I would use MC, so that is not an issue).
David