Varus is a much better midlaner. The fact that he's so mana-gated without an early Manamune /Tear on first-b sets you back a lot as far as trading AAs with the enemy ADC is concerned--can't really compete with an ADC who comes back to lane with a BF sword unless your poking skills are really good. In midlane it isn't really a problem because your playstyle is a lot more about slugging Q+E than swapping AAs with people. Varus' E is less about the slow and more about the upfront AOE damage and Grevious Wounds it applies, and is a great poking tool when maxed second as opposed to W.
That being said, he can still run bot against some team-comps and do quite well. He's always been a decent teamfighting ADC thanks to his Ult and AOE-GW, but his competence in botlane leaves a lot to be desired. I think a lot of people spite him for having a Q that scales so well with AD and armor pen, but a passive and W that favours aspd-based onhit tankbusting crap--Varus has got a serious identity-crisis which makes playing him feel awkward.
My vote is Keep Playing Varus, but as a midlaner, and consider picking up Cait or Jinx if long-ranged poking is how you like to roll in the botlane.