Sometimes they're easier to look up, and it's almost always more reliable.
Of course it's more reliable to look them up, but the point of doing a Fermi estimate here is to figure out what else you might be mistaken about. For example, if you do a Fermi estimate about how much a rocket costs and it turns out to be really inaccurate, you might learn that that's because you have a really inaccurate picture of how much engineers get paid, or how many engineers it takes to build a rocket, or how much the materials for something like a rocket cost, or...
There's a lot of background mess in our mental pictures of the world. We try and be accurate on important issues, but a whole lot of the less important stuff we pick up from the media, the movies, and random impressions. And once these impressions are in our mental pictures, they just don't go away - until we find a fact that causes us to say "huh", and reassess.
Here are three facts that have caused that "huh" in me, recently, and completely rearranged minor parts of my mental map. I'm sharing them here, because that experience is a valuable one.