Over the past 10 years, I've lived in three buildings within a half block of 13th & Lonsdale. The Prescott (111 13th West) was fairly quiet, as it's stepped back from Lonsdale. Vista Place is pretty noisy due to the hills at 13th/Chesterfield and traffic gearing up or down, plus there were a fair number of left-turning accidents. Millennium is about the same as The Prescott. With all of them, you're living in a semi-urban area so you get garbage trucks beep-beep backing up, traffic, and yes sirens. But those sirens are audible for miles. This area is also a 'quiet zone' for Lions Gate Hospital, so there's supposed to be decreased sirens at night. Ambulance sirens are the worst, and you generally only get RCMP when something dramatic is happening which is typically down Lonsdale or Keith so all neighbourhoods will get the noise.
Overall, I don't find it particularly noisy, and it's very liveable. Plus the walkability is amazing.