Battery would be a closer competitor to Ableton's Drum Rack. It also included gigs of samples from 808, 909 to heavily processed sounds and percussion. The included samples are about equal in quality to Ableton's, but Battery includes built-in FX and routing for each sample. So you no longer need to add a compressor to each sample, and an EQ, etc. It's already there, as well as effects like emulations of older sampler hardware. The downside to Battery being that it's more cumbersome to add effects which aren't already included (you need to route them to a separate output, and depending on your DAW process it on a new track).
Geist2 and Nerve are some other closer commercial quality alternatives, though I don't have firsthand experience with them. Ableton's Drum Rack is really fantastic though, and also pro quality.
Kontakt is a different beast. It includes it's own scripting engine and can easily create multi-sample instruments with different randomly chosen samples or samples chosen based on velocity or note (or both). You would use Kontakt to create a realistic sounding drum kit, or piano, etc. Things that you don't want to sound sampled. EZDrummer / Superior Drummer are similar, but specific to drumkits and you can only play with the included packs/sounds.
