This short reference bit from Ableton's Learn Live series breaks down every warping algorithm available in Simpler, giving you a clear rule of thumb for each one. Beats handles rhythmic material, Tones suits monophonic pitched sources like vocals, basslines, and synth leads, and Texture is the go-to for polyphonic content like chords.
Re-Pitch stands apart from the others: rather than stretching the audio, it keeps the sample locked to your project tempo by shifting its pitch proportionally to the tempo difference. Complex and Complex Pro cover dense, mixed material such as full song samples, but carry a higher CPU cost worth keeping in mind.