We're much more like the UK than the US in the function of government and the construction of laws, though Parliamentary Sovereignty is expressly subject to judicial review in Canada, something the UK is going to have to grapple with over the next decade now that they are no longer subject to the European Court of Human Rights.
The government can't just override the charter as they please using the language in the Guarantee. The charter allows for things like hate speech laws, but they have to fall under "reasonable limits", something the Supreme Court of Canada rules on all the time, nearly always in favour of citizens compared to the government. A recent example being medically assist death, where the Supreme Court ruled bans on assisted death violated the Charter.
The US is a free speech extremist country, but since even the US Supreme Court has ruled there are limits on speech (like threats) this isn't a night and day difference between our countries in my view. The US allows far more speech than Canada does, yet we rank higher on the press freedom index.
The thing that really lets the Charter down is section 33, the 'notwithstanding clause'. It allows the federal and provincial governments to pass laws overriding certain rights for a period of 5 years. The charter itself would likely never have come into being without it, but it does take some of the teeth away.
