It seems that DTU's are not completly comparable between service layers. When moving a workload of 95 DTU from a S3 database (100 DTU) to a P1 database (125 DUT) one can expect to see the average load on the P1 to drop below the 95 DTU.

There is no official public statement from Microsoft on why they choose to use DTU's as the measure of performance/scaling for Azure SQL DB. However, this is in line with other services like Stream Analytics and the Event Hub who's performance is also measured in custom metrics, e.g. Streaming Units and Throughput Units.

There are also eDTUs, which are related to the use of Elastic Pools. Performance wise a DTU and eDTU are the same.