Alumina is a lot less thermally conductive than AS3, but easier to clean up. There are other types that are better for CPU use (Coolermaster has a compound that's got a high thermal rating but I've never used it). Alumina is more appropriate for less heat-intensive chips.
The conductivity is the only possible "safety" issue. The specs for AS3 specifically state that it's slightly capacitive and should be kept away from points that may result in a short, but it's only actually conductive when under high pressure (I assume at that point the silver particles get compressed so much they're essentially a wire). As long as you aren't globbing it on to the point that it's oozing out all over the leads and traces, it should be fine. Unless you're building a lot of machines, there's no point to getting both types of compound for different uses.