Alright, while I generally try to avoid calling a champion "overpowered" or thinking of them as too strong, I am calling it right now that within the next few months, Draven is going to be receiving some serious nerfs.
Why do I believe that? It's quite simple, really. It's been fairly consistent for Riot to nerf champions instead of buffing the champions that counter the flavour of the month. This has been very obvious as far as marksmen go. If one gets out of line, it gets put to the back. The next marksman to get to the front of the line will generally be sent back as well.
Honestly, it feels like it defeats the purpose of having them on the team when a lot of current assassins perform their job just as well and in a shorter span of time.
The only time I would consider a marksman to be better than an assassin or any other damage dealer is when they're dealing with bruisers.
To defeat bruisers, you need sustained damage, you can't so easily burst them down. What does this have to do with Draven?
Draven has what is potentially the strongest movement speed based active ability in the game due to the fact that he can maintain it by catching axes. Movement speed is very, very important when dealing with bruisers so you can kite them. These bruisers also typically buy a Randuin's Omen is it drastically decreases the damage of marksmen that deal consistent damage via attack speed. Fortunately for Draven, he doesn't generally benefit too much from attack speed, he's much better off with making each axe hit for as much as possible versus getting enough attack speed to attack between axes(which shouldn't be happening anyway if you have 2 axes spinning).
Normally, this wouldn't be an issue. Unfortunately, it is due to Draven's passive. With Pre-Season 4 matches taking longer to end, this means that people generally get more gold and look to scaling to end games. Draven has *amazing* scaling. When he gets a Bloodthirster(which is only matched by Infinity Edge for how important it is for him) he will receive a total of 185 attack damage from it as long as he has a Spinning Axe available.
If Draven gets full build(read as 'when Draven gets full build), it won't be uncommon for each axe to hit for 1,500 damage.
The only "downside" to this is that you have to delay the game long enough for him to peak. Mind you, if you pair him with a Leona, Annie, or Thresh, it's not difficult to get early kills.
While I would like to see Draven's counters get some minor buffs. Champions like Nami for instance that can punish Draven pretty hard for catching axes out of position, or Caitlyn who can easily put a trap where his axe will land or fire off a Piltover Peacemaker to punish him for it.
That being said, if anything of Draven's gets nerfed, the nerfs should be directed at one of two things.
Either his Blood Rush or League of Draven, his passive.
For his Blood Rush, I would give it the same effect that Cassiopeia's Twin Fangs has. If he catches an axe, the cooldown is reduced to x amount(2 seconds would be good as it gives him 1.5 seconds without his movement speed buff and you can't activate it right before catching an axe to double up on the boost).
For his passive, either reduce the base gold he gets or reduce the value of each stack to 1.5 or 1. The reasoning for that is because Draven essentially gets 2 stacks(minimum) per last hit which is an additional 4 gold per last hit which doesn't really sound like much but early on, it's very easy for Draven to push a wave and get multiple stacks from a single creep.
All in all, Draven is an incredibly fun champion that is also incredibly rewarding to play. Everything about him is completely over the top, including his power and scaling.
It's entirely possible that the biggest ego in town may finally get what's coming to him.