I bought the E05 first, and really like it. After awhile I started thinking I'd like the versatility of the LD01's multiple outputs, more focused beam, and the ability to use a 10440 cell for high output. After buying and using it for awhile, I find myself still mostly using the E05.
Here's why: I love having a tiny light in my pocket that does a great job of lighting up any dark room/hallway I go into, is always there for peering into dark corners, and lasts a long time with regulated output. The E05 has an extremely wide spread of light, (close to 180°), with no hotspot. This is perfect for the vast majority of what I need a light for -- to see a wide area. The E05 is significantly shorter than the LD01, which is nice. I wish the light had a low mode for when I only need a little bit of light, though.
Pretty much the only time I use the LD01 is for it's low mode, when I'm checking on my kids at night, or don't want a bright light for reading something up close. The LD01 has a much narrower beam than the E05, with sharply defined edges. I would never have thought of this as a problem, if I hadn't first used the E05 with it's wonderful wide beam and soft edges that just sort of fade off.
The higher mode on the LD01 isn't really enough to make it a very useful outside light, so it only has one more useful mode than the E05, which is it's low mode. In the LD01, the 10440 cell puts out a ridiculous amount of light, which is pretty cool. The downside to this is that the high output heats up the light extremely fast (within seconds), only lasts about 20 minutes or so from reports I've read, and you no longer have a low mode. I don't mess around with the 10440's any more -- just keep a regular AAA in it.
So now I often carry two lights on me, with a high output light in my pack for when needed. If I only had one light, it would probably be the LD01.