I actually use both simultaneously, because (a) they're both great, and (b) each has unique features that I like. Pre-journal, each had a fairly unique niche, such that using both wasn't very duplicative at all: EDD was your mapper, and CL1 was your planet logger. Now, post-journal, they do overlap quite a bit, but (thankfully) they don't interfere with each other at all (still), so using them both isn't a problem.
EDD- - 3d mapping!!!! Three Dee Mapping!!!!! THREE DIMENSIONAL MAPPING!!!!!!!! It's slow and taxing on your system sometimes, and a bit awkward to use -- but I find it nothing short of miraculous. Also, EDD does just about anything you could ask for (with one exception....) Also, version 8 stands to be even MORE useful by auto-recording market info as you dock, and making it available for search/comparison in the app.
CL2: - It's a tiny little thing... but the odometer is just cool as heck, as is the ability to set a target system and have an updated distance-to-target number in the overlay. And I just like CL2's overlay a bit better than EDD's (although EDD's is customizable). It does most of what you could ask for (with one exception....)
The one exception is the running total of your estimated value of discoveries, which Captain's Log used to do in version 1, and which EDD theoretically can do to an extent, as it tracks individual body estimated values as you scan. It's not a mission-critical feature for either piece of software... but it was definitely useful, if only to determine how much you stand to lose when/if you screw up that neutron star boost....
Bottom line is you can't go wrong with either. EDD has more of a learning curve to it, but can do more. CL2 is clean and simple and blitheringly easy to use, but lacks some of the cool bells & whistles of EDD. And there's no reason you can't use both, if you've got the disk space for the data files.