Hello Folks,
I own a DD15 and Dynaudio S1.4 speakers, and I have tried using the sub both ways.
Using the crossover and high passing the mains is the much better real-world choice. Every major sonic attribute is imrproved when you do this, all the way through to the midrange tone and transparency.
When you use the high pass, your midrange driver is freed from having to try and reproduce the bass along with the midrange in the same driver. The amplifier is also freed from the burden of dealing with the bass frequencies.
These advantages outweigh any theoretical "more circuitry in the signal path" problems by orders of magnitude.