I used Silicon Valley Bank for a year or two. I thought I'd be running a startup, but ended up with a small business. SVB was not a great small business bank, but I can see how they'd be an awesome partner if I was running a funded startup.
One specific example is venture debt. If you raise a bunch of money from a whitelisted VC, SVB will lend you money on top of that. Maybe you raise $9 million from Accel Partners in a series B, and SVB lends you another $3 million. You get cash now without much additional due diligence, pay it back, over a few years, and keep more of the equity.
Another nice perk is working a banker you can call who understands the cash needs of startups. You can speak to a person in plain English about how your whacky business model needs to work. They see all sorts of new weird stuff, and they are conditioned to want to help you. The value of having someone understand the highs and lows of startup life, and who will go the extra mile to resolve any hiccups is subtle, but nice. Basically, a startup banker for startups is nice in the same way a farming banker is nice for farmers.
They can also help introduce you to investors. Having a banker on your side when you're raising capital is not trivial.
They're not. They do have lots of experience with VC-backed startup but the majors do too and they will all have great personal service if you have the that kind of VC (a few million+) in the bank.