I use both EDD and captains log (and did have TCE as well for system security info and stuff). All running concurrently...no problems.
Functionally....EDD I'd probably the most complete. It's almost the only tool you need. But.....the others are prettier

Now that EDD added system info I have started to drop TCE. But...TCE was better visually as it colours 'anarchy' in red and 'high security' in green where as EDD doesn't do you have to actually read it. For this trip though it's hardly a factor

hence dropping TCE.
EDD can pop up a panel on body scan showing a bunch of info including the likely TC range for the primary star.
But I'm intending to keep CL2 running concurrently for now because:
It automatically flicks between overlay and window mode.
It looks pretty like I said before and colours info about the body scanned.
Can upload to imgur automatically.....the EDD team looked at doing this but decided against it.
I usually have EDD running on a 2nd screen and CL2 on overlay.
*Ninja'd*