How is the Bitcoin node network different from the IOTA network?
As a bitcoin user, it is beneficial to run a full node because that allows you to independently validate the current state of the network yourself, without having to trust the actions or information of a third party. The user receives no monetary reward, but the ability to trustlessly interact with the bitcoin network is a very important feature, that is very core to any decentralized cryptocurrency network. 

As an Iota user, you cannot attain the same level of trustless interaction. As I understand it, Iota employs a ‘coordinator node’ that basically has admin rights to the network, so you must trust that the coordinator will not act maliciously, or be otherwise compromised. You can run a node to check transactions yourself, but if the coordinator decides to freeze your coins, having a node will not help you. 

So I wouldn’t agree with the comparison, or at least I would argue it is not a good line of reasoning. The level of trustless interaction that is enabled by running a bitcoin node is simply not possible to achieve in Iota due to the existence of the centralized coordinator position.