With what associated equipment? Are you asking about amplifiers, preamplifiers, or both?
Totally different beasts. The Atma-sphere, given the right speaker, is a wonderful sounding amplifier. It is severly limited by the speaker's impedence. The sound is very transparent and fast. On some speakers, the sound can be characterized as whitish. On others, it can be quite good.
Unless your speaker has a high overall impedence, do not expect great bass slam.
The VTL is a powerhouse amplifier. It is designed to drive the most demanding speaker with the most demanding speaker load. The sound has a bit more body than the Atma-sphere and some would characterize it as a warmer sound. Not quite the clarity of an OTL nor the speed. Amazing control for most speakers.
Now, with such generalities, it would actually help to know what models you are considering as well as which speaker you will be using.
The Atma-Sphere MA-1 should be a good match for the Talon Hawk given the Hawk's minimum impedance of 6.5 ohms (8.0 nominal). That should present no problem for the MA-1 to drive extremely well, and the speed and transparency of the Atma-Sphere should be a great match as well.
Jtinn has pretty well described the the overall sonic characteristics of the Atma-Sphere versus VTL, imo. The Atma-Sphere has more speed, transparency and definition; the VTLs will sound warmer and with more body. To my ear, the Atma-Sphere is more neutral in tonal balance.
You should be aware that my bias is towards the Atma-Sphere MA-1 given my decision to run my system with Atma-Sphere MA-2s driving Eidolons. I keep hearing from folks who bought the new MA-1 "Silver Edition" (the current production model) that they are pretty incredible amplifiers.