Pulling in things from all the answers above, here's what I came up with.
There are essentially two ways to do this:
;WITH TMP AS (
SELECT CAST(N'' AS XML).value('xs:base64Binary(xs:hexBinary(sql:column("bin")))', 'VARCHAR(MAX)') as Base64Encoding
FROM
(
SELECT TOP 10000 CAST(Words AS VARBINARY(MAX)) AS bin FROM TestData
) SRC
)
SELECT *, CAST(CAST(N'' AS XML).value('xs:base64Binary(sql:column("Base64Encoding"))', 'VARBINARY(MAX)') AS NVARCHAR(MAX)) as ASCIIEncoding
FROM
(
SELECT * FROM TMP
) SRC
And the second way
;WITH TMP AS
(
SELECT TOP 10000 CONVERT(VARCHAR(MAX), (SELECT CAST(Wordsas varbinary(max)) FOR XML PATH(''))) as BX
FROM TestData
)
SELECT *, CONVERT(NVARCHAR(MAX), CONVERT(XML, BX).value('.','varbinary(max)'))
FROM TMP
When comparing performance, the first one has a subtree cost of 2.4414 and the second one has a subtree cost of 4.1538. Which means the first one is about twice as fast as the second one (which is expected, since it uses XML, which is notoriously slow).