CTE Vs Temp Table

#CTE

• Are unindexable (but can use existing indexes on referenced objects)
• Cannot have constraints
• Are essentially disposable VIEWs
• Persist only until the next query is run
• Can be recursive
• Do not have dedicated stats (rely on stats on the underlying objects)

#Temp Tables...

• Are real materialized tables that exist in tempdb
• Can be indexed
• Can have constraints
• Persist for the life of the current CONNECTION
• Can be referenced by other queries or subprocedures
• Have dedicated stats generated by the engine.

As far as when to use each, they have very different use cases. If you will have a very large result set, or need to refer to it more than once, put it in a #temp table. If it needs to be recursive, is disposable, or is just to simplify something logically, a CTE is preferred.

Also, a CTE should never be used for performance. You will almost never speed things up by using a CTE, because, again, it's just a disposable view. You can do some neat things with them but speeding up a query isn't really one of them.