New to headphone amps --- I'm wondering .....

I recently got my first pair of decent headphones, AKG 545s, which I bought to use both at home on my main system and outside with my ipod for hiking etc. Since my pre-amp at home doesn't have a headphone out, I connect to my system via the tape out. I get pretty nice detailed sound at a decent volume that way, but have read that virtually everyone believes that a dedicated headphone amp improves sound quality. So I'm considering that, maybe in the $300 - 600 range. But I'm wondering how an amp at that price point could outdo or even sound as good as my main rig (Linn Exotic and 2500, with Renew DS) given the massive difference in price (amp pre-amp together list for around 7k). Is there something about headphone amps that I'm missing?

And if a headphone amp would help in my case, any recommendations for something that would work well with AKG 545s (very similar to 550s) with my home system?

Thanks .....