For starters, for higher-dimensional GR with $n\geq 5$ spacetime dimensions, the event horizons do not need to be homotopic to a sphere $S^{n-2}$ of codimension 2. E.g. for $n=5$, there are black rings.
On the other hand, low-dimensional GR with $n\leq 3$ spacetime dimensions is a topological field theory with no locally propagating fields.