After a couple of decades in the business, I can tell you that, level for level (cheapest phone, flagship, etc), it's about 85% carrier and 15% phone. Many of the cheapie phones (the Motorola W385 was a classic example) are deaf. Even with good coverage, you have to be in a good spot. The flagship phones are usually all pretty good and can hold a phone call through a weak signal. But I can use the most sensitive receiver made on Sprint in my daughter's house and due to a knife-edge effect from a nearby ridge, it won't pick up any signal. Yet I can use a $50 Sprint phone a block away with no problem. (And Sprint's not going to put up even a nanocell to cover one house for people who aren't customers any more).
Choose the carrier first. (Check with others on Verizon to see what kind of signal they get where you have problems, compared with what they get where you don't have problems.) If it's a Verizon problem, complain long and loudly (and very politely - that always gets the attention of someone whose job is usually being a punching bag - if you're super-nice, they'll be so happy to have 5 minutes of their day be nice that they'll do anything they're allowed to do for you). If it's the phone's problem, take it in to where they repair phones (it may not be the closest store, but ask there first where that store would be) and tell them what's happening (that, since the update, you're getting poor Verizon reception in a spot that no one else is) and let them see if they can fix it. (Flashing the older modem will put it back to where it was as far as reception goes, but still with the new firmware everywhere else.)
Then you'll know a lot more - and you'll know what kind of service your local Verizon repair center gives. (If you're looking to upgrade, maybe your contract is coming up for renewal, and maybe it's time to find a better carrier. Sprint is great all over town here, but useless to me [and their "techs" here graduated from "look for the answer in a book" Tech]. Which carrier is best is a pretty individual thing. As long as a carrier gives me coverage where I need it, I pay for the best support. I used to give it, now I want to get it.)