I partially agree with the statement about major banks, but I'm also a pragmatist. They won't be going away, so I will use them to my advantage.
I've always been an advocate of establishing relationships with several financial institutions on different levels: local banks, major national banks, credit unions and online institutions.
Having accounts and building history with national banks can help from a standpoint of establishing and effectively utilizing credit. No matter where they originate, a good deal of mortgages and business loans are eventually sold to a major bank. Plus, a solid history plus the major bank's volume of transactions can sometimes lead to a better rate.
Local banks and credit unions are useful tools, as their policies tend to be less rigid than national banks. If you're in a somewhat unique situation, often times it helps being able to sit face-to-face with the decision making loan officer, rather than a voice on the end of an 800 number.
For a normal savings account, the only place my money has been the last few years is in online accounts. The simple fact of the matter is less overhead (people, buildings, etc.) = better rates. My brick-and-mortar banks are all offering under 0.1%APY on savings; online rates right now can easily be found at 0.9%. No brainer.
I have an ING checking account. I wouldn't worry too much about the Capital One buyout in the short term. It wasn't just a simple purchase of a business unit by Capital One. As a part of the deal, ING acquired 9.9% of Capital One's stock, as well as one seat on the board of directors. I wouldn't look for too much to change that quickly.
The question I have is, how much are you keeping in a checking account to where interest rates would even be a concern? I treat my checking accounts as simply means to making payments. I generally don't keep any substantial balance in any of them.