I believe your update query works but I didn't explain well enough that the I am trying to update the UDF table and not the UserImport table.  To be specific I am trying to update the Value column.  Below is my latest failed attempt.  I'm starting to have my doubts about using CASE due to need for different information in the same column.  Thanks for any additional insight.

Update F
    Set
    [Value] = CASE WHEN F.UserID = I.UserID and F.FieldNo = 1 then I.UDF1
                    WHEN F.UserID = I.UserID and F.FieldNo = 2 then I.UDF2
                    WHEN F.UserID = I.UserID and F.FieldNo = 3 then I.UDF3
                END
    FROM UDF as F INNER JOIN Users as U
            ON U.UserId = F.UserID INNER JOIN UserImport as I
            ON I.UserID = F.UserID and I.UDF1 = F.[Value] WHERE F.FieldNo = 1