I shop around every 2-3 years or any time the rates go up more than a low, single-digit percentage. I usually swap around between Farmers, Liberty Mutual, and Progressive. I always get quotes from those three plus two independent agents in our area. The quotes from the independents are never competitive. Not even close. And the companies they recommend are small outfits I've never heard of.
Progressive is almost always the lowest on auto, but not competitive at all on homeowners. But we lose multi-policy discounts if we split it up. So last several years, the best deal is usually bundling everything together at Farmers or Liberty Mutual, including umbrella. With some more research, there might be a better deal by breaking things up but that would take a lot of work and is complicated, if not impossible, due to the coordination of umbrella with the underlying auto and home policies.
I just scan the dec pages with premiums blacked out and start emailing them around. Then fill in a spreadsheet as responses come in. The basic coverage amounts are easy enough to compare but it still gets complicated comparing polices. Nothing is completely apples-to-apples. For example, Farmers includes a no-deductible glass coverage on homeowners which we've used several times at ~$800 ea. So if we save $300/yr with Liberty but then have another $800 broken window, we would have been better off with Farmers.