Headphone amp: compare onboard/standalone

In a decent integrated (e.g., Creek, Rotel, NAD), how does the internal headphone amp compare with an outboard unit? How far up the headphone amp chain do would I have to go until I would hear a definite difference? Headphone amps with which I am familiar are the Creek OBH-11, Headroom Total Airhead, and a JMT Audio PIMETA w/ crossfeed. I need to downsize my rig and don't want to give up a good headphone experience, but need to keep costs down. Thanks very much for any input.
You might want to take the headphones you already enjoy and plug them into a few ordinary headphone jacks on integrated amps or CD players if you are lucky enough to have a few audio buddies, or a congenial store. This will give you a baseline. When I tried this I found my older Grado stock SR-200 sounded more enjoyable to me than my stock Sennheiser SD-600.
Then, I listened through the Earmax OTL tube outboard headphone amp (bought used here on Audiogon) to each headphone, and still preferred the Grado sound (even with a known poor impedance match). Of course, the sound heard became more glorious.
Although it is a cliche to say that an outboard unit is better, the simple insertion of the Grado into any jack on virtually any integrated or CDP yields surprisingly enjoyable listening.
What I am leading towards is that the headphone has a lot to do with enjoyable sound, even with built-in headphone amp.
If the Earmax is too pricey then other suggestions from Audiogon members can guide you. What headphone do you favor, and have you established an absolute top price limit for headphone amp?
if you can't spend alot of money on good outboard and headphones, say fifteen hundred, then keep your inboard and a descent pair and live with it , you probably only use headphone twenty percent of the time, and buy music, if you can buy outboard...suggest grado box with there upgraded phones...dwhittt i love headphone listening but have never found it as enjoyable as with speakers and i have gone that way back and forth for years...either buy a real good outboard and phone or leave it alone and buy music d