AsAP is quite good & convienient for me. We've been using it for 2 years and just renewed for another 2. There are 3 levels of support available - the lowest one, being 24 hr knowledge base access and regular working hours email support (called Bronze or Knowledge Base support). I beleive that the highest level give 24 hr phone support (called Gold or Premium or something like that). The reporting on the internet is simple and efficient. The machines can be grouped however you like - physical location, department, whatever. I can vouch for the e-mail support being quick and consise. One of the best things about it, is that the users can't mess with it. Without the correct key/mouse combination, they can't even disable it which is a good thing.
Supposedly there was a problem with updating on machines that do not have internet access. According to the literature this has been fixed. All my machines have internet access, so I can't vouch for the problem or the fix.
In an NT network, you can push the installation out to the clients. It may not be quite so convienient for a very large company, just because you have relativly little control over it. For example, there was an update some time ago that didn't work quite right for some clients and required a simple registry edit to fix. Without remote access to the registry of these machines, you would have to phisically go to each machine and edit the registry.
All things considered, I have been very happy with it and actually have considered using it for my home network also. I hope this helps