What I'm going to say may be heresy for some people here. Nevertheless . . .
A "better school district" isn't necessarily as good as it's cracked up to be. As we've discussed in many other threads, first, there are different definitions of what makes a "good" school district. And it's not just Realtors who should know that there isn't a single definition of a "good" school district. I've read postings here from parents who want their kids to attend racially or ethnically diverse schools. I've read others from parents who don't. (And just for the record, my son attends a racially and ethnically diverse public school.)
Some folks judge a "good" school district by the amount of money spent per pupil. But that's not always the best indicator. And here's a thought: some parents want their kids to attend a good state school. Here in Fairfax County, which many consider to have very good schools, the ratio of kids from Fairfax County admitted to Virginia universities (University of Virginia, William and Mary, and others) is much, much lower than kids from elsewhere in Virginia because those schools try to balance enrollment. Otherwise, most kids at UVA might be from Northern Virginia. That's turned into a real drawback around here. And one other example, again drawing on Fairfax County. My son went to an elementary school in the County, a school with a great reputation. Well, at the time it had an incompetent principal--narrow minded, opinionated, and dishonest. It was a terrible experience. So even great school districts can have really bad schools. (The school improved substantially after that principal left.)
And let's discuss "better" for a moment. Let's say you decide that SAT scores are a measure of "better." Let's say kids in one school district average 1,900 and kids in the next school district average 1,850. Well, the first district may be "better," but is it significant enough to affect your choice?
OK, so maybe we can agree that ranking school districts is a tricky business.
Meanwhile, my wife and I have been fairly active in school activities and PTA. Not as active as many parents, but active enough to keep close tabs on what's happening in the school, and active enough to help shape what goes on there.
Now, keep in mind that if you don't have children, and don't plan to have any, or yours are already grown, then school districts may matter less. It could affect resale value if many new buyers have kids. However, if education of your children is moot, then it may not be a critical issue. I have a close relative who doesn't have children. She recently bought a house, and selected one she liked in a neighborhood she liked. She doesn't know or care about the local schools.
Beyond that, remember (speaking here as a parent) that kids are shaped, formed, and educated by far more than what goes on in a classroom. Yes, a quality school is important. But my kid spends 6 hours in school and 18 hours outside of school 180 days a year. During those 180 days, we talk with him, play games with him, and just spend quality time with him. When he was younger, we read to him and helped him with homework. Now that he's older, we have great discussion and debates with him. During those days when he's not in school, we might take him places. We visit relatives. We go to museums. He takes classes in karate and grappling. (Before you start talking about all that costing money, it does cost some. But he's worked enough at karate and grappling that he now helps out at a local studio and gets his lessons at no charge.) Some of his friends with licenses work, and they're learning good life lessons along the way.
The point is: Kids are not shaped just by the 6 hours they spend in school for 180 days a year. Home environment and parental involvement count for far more.
Sure, if all other things were equal--home style, price, nearby amenities, length of commute, tax rates in the two jurisdictions (to pay for those schools)--I'd probably choose the house in a "better" school district, based on my own definition of what a "better" school district is. But those other things are never equal. So, "better" schools are one factor to consider, but only one.
Hope that helps.