Kare-kare, when made from scratch, derives much of its taste from annato and ground peanuts so it’s relatively mild tasting. The bagoong gives it an interesting complementary flavor contrast - like Noel, I prefer my kare-kare with bagoong.
Ah, yes, bagoong. Both patis and bagoong can add a shot of salty umami goodness to food. Much like garum or the modern version, colatura di alici. Bagoong can be much more pungent, though. I find the most pungent versions are the ones like a thick liquid, closer to true garum in that it’s truly comprised of the liquid the fish has fermented in. However, many Filipinos’ idea of bagoong is the paste made with krill or tiny shrimps. This is the kind you find in local supermarkets, and Asian groceries in the US. There can be a big difference, though, between commercial bagoong and the home made variety. Pretty much all the bottled bagoong in supermarkets is jacked up with MSG - not a good sign. As to patis - one can have an extended discussion about the taste of Philippine patis compared to Thai or Vietnamese, best not go down that rabbit hole.