Hi,
I am not totally certain what you mean by a "flat" sound, but having heard many CSB recordings, I think I know what you mean. The HEB microphones are definately a major step-up from the CSB mics, and are much more stealth-able.
As Brian mentioned, both are omni's.
The Core Sound HEB's are either DPA 4060's or 4061 microphones wired into a battery box that core sound makes. I "had" a pair of the 4060 HEB's, but ended up sending the 4060's to DPA to have the microdots put back on so that I could use them with the MMA6000 preamp, which was the best choice I ever made. There is simply no comparison between the core sound battery box recordings and the recordings I made with the MMA6000. The MMA6000 seemed to lift a veil that was present when using the core sound battery box. Now, maybe that is more due to the preamp boosting the level into the recorder, but I also think DPA knows their microphones and how to power them much better than Core Sound does.
I would recommend that you not buy the Core Sound HEB's, and instead buy the actual DPA microphones (either the 4060's or the 4061's). You can then either buy the DPA "battery box" or the DPA MMA6000 preamp depending on your budget. If I had to do it all over again that is the way I would go. Cascade Media is a DPA dealer, and I would recommend them as a starting point for you. I think you will be much happier with that set up in the long run, and have many more options for upgrading if your budget right now only allows for the microphones and battery box.
Core Sound is charging a premium for their battery box and the "matched" microphones. I believe that you can get DPA to match the microphones for you. There are other threads on the list about how close stock 406x microphones are (when bought new - not the used eBay ones). The only other thing that the HEB's do give you are the microphone clips - which are worth about $50USD for the pair ($25USD each).
Hope this helps.
T.