FIP is the best one to look it. It just tries to assign pitcher value to the ones doing the work. So Hudson has a poor FIP and better ERA, because he induces a bunch of groundballs of which the very good Cardinal infield defense takes care of and doesn't really strike anybody out. That's why Fangraphs WAR uses FIP instead of ERA (baseball reference uses ERA), it gives Kolton Wong/ Paul Dejong that value on defense instead of giving it to Hudson, since they did the work.
Just to add on to what Tisdale was saying, FIP stands for “fielding independent pitching” and tracks how pitchers do when the ball doesn’t go into play. Which means strikeouts, walks and home runs.
Studies have shown that over a pitcher’s career the swings in FIP are far less than in ERA, which should make sense since a huge chunk of variables are taken out.
FIP is indexed to the season ERA. In other words, league average FIP will be the same as league average ERA.
Generally, the difference between FIP and ERA can be used to see who gets more or less help from his fielders and/or who’s had a lot of good or bad luck. To distinguish between fielders affecting the pitcher or luck, you usually have to look at the other pitchers in the staff. If everyone has a much better ERA than FIP, you can generally assume they’re being helped by really good fielders.
Guys who induce a ton of soft contact will usually have a much lower ERA than FIP over their career. Kyle Hendricks is a great example... 3.10 career ERA vs 3.55 career FIP. Hendricks is also a good example of how FIP tends to deviate less than ERA over the course of a career. The difference between his career high and low for FIP is .68. That difference is 1.82 for ERA.