I had the DIs and have since upgraded to the DI SEs, but I do not yet have a fully informed assessment of the differences because my SEs are still going through the break in process.
Based on what I have heard so far, I think what you get with the SEs in a nutshell is a more dynamic, more resolving, speaker, with deeper, more impactful bass. The SEs are REALLY going to tell you what is going on upstream in your system, so any changes--positive or negative--are going to be more pronounced with these speakers than with the DIs. Some might say the SEs are "less forgiving," but it may be that they are just more accurate.
If any of this sounds dismissive of the Double Impacts, please understand that I am speaking here in relative terms. The DIs were outstanding in my system, and in my opinion a crazy good deal at their price point. I could have lived with them long-term, but stumbled into a good deal on the SEs and jumped on them.
As I said, my pair still has a ways to go to get through the ups and downs of the break-in process, but my view is that the SEs just give you more than the DIs and are speakers you can grow into--they'll get better and better as you make other improvements in your system down the line.
I hope this is helpful.