Very generally speaking the headphone socket on an integrated amp will be ok, but won’t have had a huge amount of thought or expense thrown at it. Some of the very high end amps have great headphone amps, but usually not so much.

A separate headphone amp can make quite a big difference, especially if you have a pair of difficult to drive headphones or some such as the one on the integrated amp will be designed generally for easy to drive headphones.

Where they can help a lot if you re really into your music is coupled with an iPod, iPhone, media player etc. The Apple stuff and most other recent smartphones have the ability to send a line-out signal from the dock port which you an run through a headphone amp and significantly improve the sound quality over the headphone socket. I use a little Fiio E7 with my iPhone and the change is quite appreciable – a much more open sound space and lots more detail. The headphone socket sounds really compressed if you go back to it now.