Currently I use epic4, which is so near to being ircii really that we might as well consider that it is – certainly the main reason why I'm using it is because its more stable than ircii rather than any funky features.
Here we have a (by now rather old) picture of a typical IRC session, with annotations. In practice that's only half the picure however, since I have another "frame" akin to this one that exists on a different screen(1) window. Also note that it's a command-line application not a graphical one, which is important as it means that I can run it within screen(1) and have a certain amount of relocatability.
The ordering of windows within each frame stays the same, and which window appears in which frame stays the same, and you can shift the context between them using ^X p and ^X n (although I'm not wedded to those hot keys).
Obviously I'd also like it to have a seamless interface for telling it which windows to put where with which channels on which servers in, but in practice I appear to have had insufficient effort to ever set things up in any client I've ever used, so
seamlesswould have to be pretty bloody seamless. And it might be nice if it would do charset translations, but in practice I can do those in my head for any character I can display everywhere anyway (from long exposure), so that's not really an important issue.
Oh, and it shouldn't start blurting colour all over my display either – it should use my existing foreground and background colours for everything, with a possible exception of using "bold" for the status-bar.
People who are about to say "use irssi" should note that none of the last 5 people who said that to me were able to produce a setup that fulfilled even those requirements (and I'm sure that in practice I have hidden requirements that haven't been made obvious during my forays into other clients, but I have no idea what they are and I'm happy to work with anything that supports the windowing paradigm that I'm used to).
Oh, and people who are about to say "use bitchx" should provide both (a) stuff to turn the colours and offensiveness off and (b) some example of any actual benefits of shifting from epic4/ircii to bitchx thats hidden by all the colours, offensiveness and warclient tools.