^^ as much as I agree to some extent with the above statement, I don't with the HD600 and above. If by full size amp, you mean something with a different flavoured sound, then yes... in a way, the mains amp will be better - so long as 'better' means 'has a different sound signature'.
Two neutral amps, however at exact volume-matched levels will sound the same. There could be differences: one could have better L/R separation or another more/less distortion, but they should sound (and do) almost the same.
If one has a lot more distortion or crosstalk, then you get into big differences, but a portable which is built well can drive the HD650 and HD600 very, very well, better in fact than some full size amps.
Mix tubes into the equation and you really start to get a different sound, but it doesn't mean better, just different.
If we are talking about really hard to drive headphones, DJ1pro, AKG 701, then a portable will probably not do justice to the headphone which has a lot more swing throughout its FR to impedance - but maybe.
IEMs are also hard to drive (or can be), but headphones especially above 200Ω are easily driven from almost anything. Whether you like the sound coming from them is another thing, but they are pretty easy to drive.