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.

I) For starters, for higher-dimensional GR with $n\geq 5$ spacetime dimensions, an event horizon (which always has codimension 2) needs not be homotopic to a sphere $S^{n-2}$. E.g. for $n=5$, there are also black rings.

II) On the other hand, low-dimensional GR with $n\leq 3$ spacetime dimensions

• has identically zero Weyl curvature tensor;

• is a topological field theory with no local physical propagating fields, i.e no gravitational waves.