In bitcoin you don't get paid to run full nodes. Only the miners get paid for verifying transactions. Verifying transactions is done by the users themselves with iota, so there is no need for miners and no need for fees.
Unless the cost of verifying transactions is zero, this just means that the cost is now measured in CPU cycles at the client. In the end, this may be higher than whatever you pay with Bitcoin, depending on how much work you need to do. This is what I mean by "making fees implicit" - there's still work to be done, but not putting a price on this work doesn't mean it's free.
Then there is a price; it's just measured in watt-hours of energy spent instead of denominated in cryptocurrency.