Well there are a few factors to take into account, mainly the nature of the software and the target audience/consummer.
If the consumer is likely to be tech savy, they'll want to be given a certain degree of control, if not, they'll likely expect you to do everything for them.
Personally I hate resident processes, such as the google updater or the adobe auto updater, I hate a program being there running consuming my computer's resources while I'm not even thinking about their software, adobe reader is probably the worst example of this, you open it what, once every coule of months? meanwhile adobe has a resident software active on your computer full time, why? why does that need to be there? Steam on the other hand, can be set so it doesn't start at bootup and will only update when you start the program.
Thats another issue for me, unless the update is absolutely required for the software to function, when I open the program I want to use it, making me wait for an update is an inconvenience, if the update is optional, I would prefer to delay it to when I close the application and no longer care about it. Thats the way I handle windows updates, I apply them once I decide to shutdown the computer, not when I want to use it.
Taking the user to a website is pretty old school and annoying, its not even necessary, you can trigger the update download and instalation without going anywhere, do that.