I'm trying to learn some algebraic geometry, and of course I came across the notion of open/closed subschemes of a scheme $X$. Everytime I deal with open subschemes, I feel way more comfortable, becauce open subsets $U$ feel "better" in the sense that the induced topology is somehwat "nicer" - opens of $U$ are open in $X$, U doesn't loose properties as being irreducible and, in the Noetherian case, quasi-compactness... - and the relation of the structure sheaves $\mathcal{O}_X$ and $\mathcal{O}_U$ is of course very easy. For closed subschemes $Z$, however, I feel a bit unease because from a topological viewpoint closed subsets seem to me not as "nice" as opens - influenced of course from analytical viewpoints - and also the structure sheaf $\mathcal{O}_Z=i^{-1}(\mathcal{O}_X/\mathscr{I})$ for an ideal $\mathscr{I}\subseteq \mathcal{O}_X$ looks more complicated. We have one sheaffification in the quotient and one sheaffification for the pull-back - my gut feeling is that it's "harder" to get a hand on this thing.
As to come to my question, I "like" open subschemes more than closed subschemes: is this valid, or are closed subschemes by far more important in applications than opens? And, of course, are closed subschmes even "harder to get a hand on" than opens, or is this just an impression at first sight?