I have to say, I have been playing Eb almost exclusivly for the past 2 pantheons. I'm doing pretty good, I have about a 70% win and stay around the 200-400 rank range.
Everyone here seems to be focused on what Eb is good at, or what he can do. Let me flip the conversation a bit. These are the situations I tend to avoid because I know they are risky.
I avoid standing next to a tower when another DG is within striking range. DG's that can stun you or interrupt you when you are next to a tower have a better chance of killing you than in any other circumstance (outside a 2on1 gank that is). Forts don't do crap, so don't try and take Eb 1v1 if all you have is a fort close by. Get 2 DGs on me and I will move, otherwise your food. Arrow towers hurt me most, of all things in the game. In fact, I hate arrow towers more than UB for damage. This becomes a non issue at about lvl 9 though.
Getting priests only helps me as I can kill them too easily, so don't buy priests until you can get cats as well. That only helps me lvl past you.
Another thing that hurts me is if you don't let me creep kill during lvl's 3-7. If you interrupt my ability to lvl early, then it is harder to (relativly) to play the middle game. If 2 DG's are on me early game, then that can hurt pretty bad. Just harrass me and don't let me dominate a lane. Otherwise your toast once I get bite 3.
I am sure there are more situations, but right now that is what I can think of.