Yes it depends, but to sound good, or even to just attain a reasonable level, some headphones need a lot more power than the Clip+ can offer. Sound quality in terms of fidelity may be good, bad or indifferent but if the desired level can't be reached then the sound quality is compromised.
If Tanjent is using Clip+ and relatively high impedance 'phones of known high quality and is dissatisfied then the obvious thing to look at to remedy that is amplification or an IEM that is more sensitive and with lower impedance i.e. more compatible with the source. Maybe it is something else but starting with the obvious is not so silly.
As to what player currently available might be better I can't say except it is going to cost lots more than the humble Clip+. My other players which can drive slightly more demanding 'phones are really old. I would hate to be buying a new player these days because beyond the well specified, low price players like the Clip+/Fuze range there is an awful lot of unappealing fashion-victim crap until you spend really big or give in and buy an iPod and let Apple dictate your file formats, metadata schemes, software choices etc etc. Perhaps the exception is the Fiio X3, not sure.