From a purely roleplaying standpoint, you can play it off that the long-lived races have something that the short lived ones don't: Patience.
Essentially, I like to think that elves, biata, etc feel like they have all the time in the world to learn or to do things. Its almost a foreign concept to humans in real life, as it would seem (at least where I live on the east coast, near urban areas) that everything is 'do-it-now-get-there-now-have-stuff-now-now-now'. So, the perspective of 'having all the time in the world' is the way I feel about long-lived characters. I mean, if you had 50 years to be able to perfect the way you crafted/wrote/did something, wouldn't you take it?
My sarr's just hitting the crest of the 'in the prime' mountaintop, and I roleplay her accordingly - I've started to roll my shoulders before going into a fight, complain about an old injury, etc etc. She's a grumpy cat who's starting to slow down, and is roleplayed accordingly.
On the other hand, my elf left home at a relatively young age, so she's still rather impetuous and 'almost human' in the way her decisions are made, because to me, that impatience reflects the 'I haven't been around for 100 years.' after she hits her first century, I'm sure her perspective will change.
Another thing to look at too, is when playing an older race, you could've done other things that are not related to your character card. You could've been a fisherman, a baker, anything in turn that would allow you to build a character who is level one, but at an elder age.
Regarding long lived races played by people getting older, I agree with Mike. I think the life/stress of an adventurer is something wherein that could absolutely add to the age of your character. A few grey hairs here and there from the lich who almost took your head off when you became an adventurer is added story - something I think that would get lost if everyone aged at the same rate, along with a lot of the personality perspectives of Orcs and other short lived races versus the long lived ones.
-Ali