Prefer charset declaration in HTML meta tag or HTTP header?
To understand what modern browsers do, you should start reading at http://w3c.github.io/html/syntax.html#determining-the-character-encoding
Steps one and two are most relevant to the question. They say
If the user has explicitly instructed the user agent to override the document's character encoding with a specific encoding, optionally return that encoding with the confidence certain and abort these steps.
If the transport layer specifies an encoding, and it is supported, return that encoding with the confidence certain, and abort these steps.
which means that the real HTTP header takes precedence over everything except user over-ride.
Beyond that it can get complex. A byte order mark, can for example, take precedence over the meta tag.
UPDATE: Since this answer was written, the spec changed (around mid-2012) so that the byte order mark now takes precedence over the HTTP header.
There's simply no answer to this. The author of the page has committed an error by giving conflicting information. Which one is correct may as well be decided by a coin toss.
In general, I'd prefer the HTTP header as the primary value. The meta tag is just meant as a fallback anyway. If you want to follow any logic at all, first try to decode the document using the charset specified in the HTTP header. If that clearly fails, because certain bytes are invalid in the given encoding, try again in the charset specified in the meta tag, if any. If that still fails, all bets are off.
If neither fails but the encodings conflict, either involve a human or try some statical analysis on the decoded text, which may tell you which is more likely to be correct.