Good to hear that I'm not alone with a similar and somewhat unexpected difference.
In terms correctness (as in flat frequency response), I'd say that nothing beats measuring then. If that isn't an option, I'm squarely in the 'what-makes-your-music-more-enjoyable' corner. More of something isn't necessarily better, as balance is what you're after. On the low end, it depends mostly on if it is the very lowest frequencies as many setups (normally not transports however - in my case from the OP it's my speakers) have a rolled off bottom. Thus - extension is at least what I have found more important. Systematically go through your music and find stuff that tests particular ranges by for instance having only voices (i.e. singing 'a capella'), or having a certain instrument (or maybe two/three that aren't too close in terms of where they operate) that is central to the overall piece/song. There are good guides (google this) for which instruments cover which frequency ranges, so this can be helpful if you find one area that is different sounding than another, because what you're looking for is to nail down what subjectively sounds most natural in different frequency ranges.
In regards to your dilemma - I'd easily say that the point brought up earlier in my case that the hardware implementation may be more or less successful is a probable cause.