CTEs…

• 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.

CTE

WITH cte (Column1, Column2, Column3)
AS
(
    SELECT Column1, Column2, Column3
    FROM SomeTable
)

SELECT * FROM cte

Temp Table 

SELECT Column1, Column2, Column3
INTO #tmpTable
FROM SomeTable

SELECT * FROM #tmpTable

Example

CTE

temp table

Refer to or reading

• What’s the difference between a CTE and a Temp Table?
• which-are-more-performant-cte-or-temporary-tables