It is harder to say anything definite about Eddie Current as there are lots of rolling options for most of his amps that makes it hard to pin down an amp as having a specific sound. I also sold all my EC (excpet the incoming Electra) in preparation for the Leviathan so I'm running on aural memory, which is fickle at best. That said...
They definitely share some traits - low noise floor, great low level detail being the two most obvious, and they also seem to have a similarity in terms of optimal headphone pairings.
They do differ though in a few ways - EC (I'm referencing the Balancing Act in particular) has unmatched soundstaging - I've always imagined this has to do with the HF heater on the DHT deal they have going. The ECP amps are all quieter with more sensitive headphones though EC is no slouch in this department. The L-2 as a "tube amp" is even closer to what is traditionally though of as "solid state" than Eddie Current which is already pretty non syrupy for tube sound. While Eddie Current amps are by no means "lush" (except possibly the ZD which is closer to "lush" than his other amps) they are more so than the ECP amps.
That said, taking as an example the keyboard on "Everything in its right place" from Kid A which definitely has a warm, enveloping cocoon-type feel to it, the L-2 will definitely render it just so even though it is not particularly "warm" - it won't take any of the "magic" out of what already exists in the recording. The BA could sometimes interject it's own "magic" into the recording even when the source material didn't seem to have it, which I found phenomenal but I could see that bothering some purists.
Ultimately, the Balancing Act has more resolution/microdetail than the ECP amps or any amp I've owned. It is slower than the L-2 though, and I'd be willing to bet it has higher 2nd order just based on sound though that's not necessarily a bad thing.
Eddie Current amps have the ability to sound aggressive though they can also be laid back depending on tube choice. ECP is slightly closer to the laid back side of the spectrum.
Lastly, while all things considered I personally prefer the looks of something like the Balancing Act to the ECP amps which is a subjective thing, the ECP amps have better build quality, both inside and out. Its very hard to get a "perfect" EC amp without any small physical defect anywhere on the product. Chances are there will be something small somewhere, whether its some small nicks or scratches or some other small thing - its part of the charm, but I know some members more OCD than me who it has bothered. The ECP amps are perfect in that department.
So, even if I had one brand already, I would not consider the other redundant. However, if I already had one, was happy with it, and was now looking for say an ortho amp, I would look elsewhere.