"it depends". Is anything on your current server maxed out? Memory? CPU? I/O? Diskspace? If you answer "yes": is the maxed out resource required by both components (web tier and db)? If it is you might gain, depending on the network connection (latency, throughput) of the connection between the two machines.
If apache maxes out CPU and db maxes out memory you might not gain much by separating the two.
These are just examples - to really answer your question one needs to take a lot more aspects into account than you name.