I have always used a big beefy solid state class-A amp for driving headphones. All my impressions are done on class A amps and both my portable amp + full size if that headphones is designed to be portable. I am not a big fan of tube amps myself so I don't tend to use them. Maybe here is why our opinions are different. I found the headphone "amp" out on my Essence mediocre at best.
I haven't heard the HD448 and not likely to do so ever, so I won't be commenting on it.
Amps that I normally use for testing, Burson HA-160, B22, Luxman P-1u and HA5000 for Audio Technicas.