PHPStorm plays nice when any framework. The issue it's going to have is when Frameworks do not clearly document, or when they make bad decisions about things. You can, of course turn off different levels of inspections to account for the project you are working on. However, I've found that for the most part, if PHPStorm is flagging something like "undefined method," it's essentially saying "you are hoping that this works as expected." It's a form of static analysis.

I'm not surprised that an old CodeIgniter project flagged these issues.

As for vi, I use vi every day as well. I switch between that and PHPStorm. It depends on the context that I'm in. Both are wonderful tools. But I can assure you, auto-complete is a basic feature of PHPStorm. It's akin to 'set nu'.

Edit: This comment comes off as a bit snarky. It's not intended to be. I think JetBrains and it's line of products are excellent, and I've only ever had good experiences with them. I wouldn't want my comment to reflect poorly on them.

There is normally a little bit of setup to do in getting it to detect objects, methods, and variables. Normally I have to add some stuff into the libraries section. (Sometimes this doesn't work when there is a lot of indirection.)

It does play nicely with Zend and Silex (and other composer-style frameworks). I'm not sure about Symfony or CodeIgnitor.

I must say I really like PyCharm as a Python IDE. Tricked out vim is just too hard to install onto new machines, etc.

I have been using PhpStorm for a Symfony2 project since 2-3 months and the integration is very good.