Yes, we have the same ideas. I think EOS is not an opponent of Ethereum. In the future, there are only two opponents of Ethereum, one is NEO and the other is ADA.
There are many more blockchains that rival Ethereum, for instance Wanchain, ICON or Rchain and many more in development that claim to be able to do excactly what Ethereum does, plus offer a better scaling and more features. Time will tell.