Which web frameworks should I focus on to make myself the most well rounded and to be able to solve the most problems as a web application developer/architect?
Being an expert web developer isn’t about which framework you know, it’s about the fundamentals. It’s important that you know how the tools you are using work, so you can fix things when they break—Joel Spolsky’s law of leaky abstractions is a great essay about this: http://www.joelonsoftware.com/ar...
Then there are the systems architecture concerns: persistence, sharing, replication, when and where to apply both SQL and NoSQL technologies, load balancing and so forth.
The web framework you use ends up being a relatively small part of the overall problem—it’s just the bit that passes an incoming HTTP request through to your custom code, then hands the resulting response back again.
So as long as you pick something that doesn’t prevent you from getting stuck in to the underlying details (a closed source framework would be a bad idea here) you should be fine.