You can't and really shouldn't compare the two for the same workload; they're designed for different things based on completely different architectures. As such, DTU and DWU are not comparable measures. Also, how deeply have you looked into the technical differences? The high level features are not the major issue, details are what might wreck your app (e.g. can you live with a limited TSQL surface area or transaction isolation level?)
Azure SQL DB is intended to be a general purpose DB as a service. The few feature gaps aside, you should think about Azure SQL DB functionally the same way you do SQL Server, minus a lot of the administrative tasks and with a different programming model. Works great for OLTP apps and most reporting apps (or mixed) but not so great for complex analytical apps against with very large datasets (can't really store that much in SQL DB anyway).
SQL DW is intended for data warehousing, analytical type workloads. Its MPP architecture is particularly well suited for complex queries against very large data sets. It will not perform well for typical OLTP applications that have lots of small or singleton queries especially when it's a mix of insert, update and delete operations. If you get a trial instance of SQL DW, you can easily test and verify the behavior for your workload compared to what it currently looks like on SQL DB.
SQL DW also has some limitations on its TSQL surface area, types, concurrency, isolation levels (deal breaker for almost all OLTP apps), etc... so be sure to look into the documentation to get the whole picture as you evaluate feasibility. It might work great but I suspect it's not the best solution if you're running an OLTP workload. Reporting/analytical type workloads however might find a happy home in SQL DW.