Vengeance is about a Frenchman who travels to Hong Kong and Macau to avenge the murder of his daughter's family. The Memento-like riff is that he is losing his memory and so needs to take photos of people to remind himself who they are. It takes a long time before the filmmakers find a way to use this idea creatively, and then they use it really badly. What's annoying is that the movie doesn't need the memory loss lead at all, the whole movie still would work well if the guy was compos mentis, you still have a fish-out-of-water lead character, and you still have lots of material about loyalty and brotherhood.
Bloodthirsty vengeance is obviously a really bad idea, and so if you're going to make it the theme of a movie, you need either a strongly pulpy feel to the movie, or you need really stupid characters; maybe make it a samurai movie, as the sort of moral codes that existed centuries ago would make sense of the characters and their motivations here. As it is, this movie just doesn't make sense. Some of the narrative conceits are weak, like how the lead character comes across some assassins for hire randomly in his hotel. The movie also had really bad CGI, you could see the blood spurts each time someone got shot were amateurish.
I ended up being pretty annoyed, it just felt like someone had torn a first draft script from a scriptwriter's hands and just started shooting with it. Johnny Hallyday (rest in peace), is a picture of pain, but because he's been worn down by age and strife, not because he's acting it, there's nothing expressive about what he's doing in this movie. It comes across like he's involved so that the movie still got co-production money. According to Roger Ebert he was a last minute substitution for Alain Delon.
I won't deny that the movie has effective moments, the set piece at the barbecue spot at night is really good, although even that has a really stupid moment (improbable boomeranging Frisbee). I've recently watched Takashi Miike's Black Society Trilogy, and this effort from Johnnie To is absolutely light years behind those excellent movies in terms of quality. Somehow this was accepted in competition at Cannes in 2009.