I couldn't vote as I love (and hate) both shows equally.
Extra Credits is a show I enjoy watching for their refreshingly upbeat approach to discussion, with every episode not only looking at the effects of an issue but also trying to find the root cause and at least one constructive solution. (Note I said TRYING; just because you disagree with their solution doesn't negate the fact that they were trying.) The down side is that there is a sense of disconnect that they have with the viewer that can come across as patronising or aloof but I put that down to the politician syndrome. Their scripts are written by James who (if memory serves me correctly) works within the industry and as such has to be very careful what he says publically for fear of effecting his livelyhood in the same way you will never hear a politician say what he really feels. There will always be a certain level of spin.
Jimquisition is a completely different kettle of fish. Jim is on our side of the fence; he's one of us, a gamer. He is also clever enough to realise that WE are his livelyhood and as such he not only tries to reflect our feelings on game related mattters but also listens when we have criticism. The down side to this is that, in the videos at least, Jim has a tendancy to use sensational or one sided arguments as a way of generating debate (or trolling for short). Like Yahtzee, his videos are the desert to the meat and potatoes of his written content.
Both shows have intelligent, insightful, thought provoking moments but both have inevitable flaws drawn from the unique perspectives of the writers.