Good question.
But I reckon the lack of response to it so far, suggests it's one that not many people give any thought to.
Indeed, if you read through the WHF review of the (2nd generation) Tivoli, there's no mention of headphones whatsoever.
Amazing really, because, it's only got a single speaker - for 300 quid, maybe it can play out stereo via a h/p socket?....but you wouldn't know from that review.
Anyway, in answer to your question, I would say that provided your headphones are decent enough, then you should hear differences.
Try to check the specifications of any radios you're interested in (if you can) because some pocket radios may not have enough drive for high impedance headphones.....and you need to make sure the radio is at least stereo!
Unless portability is essential, web radio via a DAC / amp, or just an analogue tuner into a dedicated headphone amp.....would give you better quality - if your headphones are up to it.