Note. . The suggestion below works at the time of publication. This behavior may change in the future.
Today there is no easy way to do this. I added a function request to find the purpose of the service through TSQL. As a shortcut, you can run the following command:
SELECT
    name,
    recovery_model,
    recovery_model_desc
FROM
    sys.databases
WHERE
    name = DB_NAME();
If file recovery_model = 3 (SIMPLE), this is the SQL Data Warehouse database. If restore_model = 1 (FULL), this is an SQL database.
May 2016 update:
The following query will return DataWarehouse if you are connected to an Azure SQL DW database:
SELECT DATABASEPROPERTYEX(DB_NAME(), 'Edition') As Edition
# 2:
sys.database_service_objectives DMV, :
SELECT
 db.[name] AS [Name],
 ds.[edition] AS [Edition],
 ds.[service_objective] AS [ServiceObject]
FROM
 sys.database_service_objectives ds
 JOIN sys.databases db ON ds.database_id = db.database_id