The Elph 300 HS produces generally excellent snapshots. Photos do get softer and noisier above ISO 200--typical for point-and-shoots--but ISO 400 and 800 are still very usable. The noise and noise reduction are well balanced so you still get good color and detail at these higher sensitivities. Colors desaturate some at ISO 1,600 and 3,200, subjects look very soft, and detail is greatly diminished. While you might not want to view them at larger sizes or heavily crop them, the high-ISO results should be satisfactory for Web or prints at small sizes.
Compared with a camera with a similar sensor and lens, the Sony Cyber-shot WX9, the Elph 300 HS may have a slight edge, but it really depends on your needs and expectations. Both drop off in quality at ISO 400. The Sony's noise is slightly better, but its reduction smears details; the Canon is noisier, but it retains more detail.
(Note: These were taken with the Canon PowerShot A3300 IS, but the 300 HS produces similar results.)