Did a project in cakephp a while ago, using mongo and such. It was alright.
Currently building a different site using yii2, twig, fb api, and mongo. This wasn't fun to set up on my windows machine. Took 2 seconds on ubuntu hehe.
I am enjoying yii2, but this time going without anyone to instruct me it is slower going.
I chose mongo as a storage engine simply because it is generally very fast. The way it's flexible storage system is perfect for my needs, because I don't want to constantly add many field types and such things. So I'll design so that Each user is a silo with all their data contained.
User A will only ever see User A, so this makes this great. Not the worst setup for data collection either.
Now Wordpress. For most sites I'll use wordpress, advanced custom fields, maybe(probably) acf repeater, wp super cache, custom implementation of twig. Grab bootstrap, jquery and start building a theme, or use a base skeletal one to speed this up.
Generally as a rule with wp, if I can throw it up and get both the cms and the functionality desired working faster than a framework, then I will.
Expression Engine. Sigh... While I've hated this cms from the day I began using it, It was my job to not only to become proficient, but to become an expert at using it. I can't call myself an expert so much as highly creative. I do have a patch I contributed to a while back, and I have done a lot of stuff in stack exchange. ok So here is why EE is on this list. We wanted to land a client at work, but we REALLY wanted to land it. So we took his idea, and we built a mock up, functional and non-scaling version. We threw this on a digitalocean $5 box with ssd and that was the magic. We built this mock up in two days and it landed us the client.
My point is, you can crank something fast out in EE. Especially with its hidden relational db type of powers.
So................ I use whatever framework suits the project at hand best, and which framework is mose efficient to use (client needs included), and finally, of the ones left, whichever we prefer.