I also use both Indy and ICS.
Most of the time I prefer Indy because implementing sequential type of protocols with it is very easy (the request runs in it's own thread so you simply Read/Write to the connection, really easy). Using Indy requires solid knowledge of threading and synchronization. Unlike Runner I like how Indy uses Exceptions to handle "exceptional" stuff because it allows me to concentrate on the normal flow of the protocol (I use try-finally blocks to make sure I deallocate resources).
I also used ICS in a application where Indy simply failed: I used it for an application that implements an TCP/IP proxy. Using ICS was simpler because of it's non-blocking nature. I was able to "proxy" TCP/IP protocols that I know nothing about, so I have no idea how bytes would flow from one end to the other. Indy failed in that scenario because in Indy you're ether reading or you're writing, you can't do both at the same time. Using ICS to implement an sequential-type protocol is a bit of pain: you essentially need to use state-machine logic, brake the protocol in small bits, keep flags laying around so you know where you are in the protocol. An big plus: François Piette, the author of ICS, is active and very helpful on a number of forums and mailing list, and is very prompt to help with anything related to ICS.
For me, if I need to do something with TCP/IP, the decision path is very simple: Can it be done with Indy? Then it's Indy. If it can't be done with Indy then it'll be done with ICS!