The "Button Device" trigger type has been pulled from Rule 5.0. What it was, as you likely know, was basically a beefed up version of Button Controller, which was also available as a separate app (aside from a few releases where it was briefly returned in favor of just rules--but it came back). It added conditionals and a few things that plain BC did not have.
New in 2.2.8 comes a new version of Button Controller (version 5), which has nearly the same capabilities that rules do. It is also internally structured a bit differently, as you may notice that it now creates "grandchild" apps in your apps list, one for each button action you have configured (this was to facilitate things like repeats, where it was previously unclear whether you could cancel or modify one from another button action and apparently hard to enforce the desired behavior; they are now all separate). I would say that it is the recommended path between the three things under consideration here--"old" Button Controller (you can't create new child instances of these anyway), Rule 4.x with a "Button Device" trigger (you won't be able to create new Rule 4.x instances after firmware 2.2.8--but no need to move existing ones), and Button Controller 5.
Do note that you still can (and always could) create rules with a specific "Button" event as a trigger. In most cases, this is probably not what you want--certainly not if you want a single place to define multiple actions for different events from the same physical device. But it can still be useful in specific cases.
