No transaction is ever free. In EOS cost it is paid out through 5% inflation to miners. The big advantage is the EOS distribution which gets many many people invested in the block chain. The other advantage is if they take the money raised and invest it to create the best dApp ecosystem then it will become popular. Similar to the App Store selling iPhones.
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There is also a 1% fee on RAM trading which may be enough to pay the block producers on its own and there might not be any inflation at all when it's all said and done.
(Disclaimer: I also own both NEO and EOS) The NEO council still holds 35M NEO that will use to invest in projects and partnerships. So also in this point there is little difference between NEO and EOS.