Funding makes a HUGE difference in the available quality and quantity of instruction. Most of the "big name" schools you see winning contests and performing "cohesive tight shows" have not only several band directors on staff, but also they bring in techs to work with the band, specialists to run sectionals, private lesson teachers, etc. Having all of these personnel to split the kids into small groups and give individualized, specialized instruction makes a huge difference. You can't have that instruction without funding.
Even without additional staff, funding can make a big difference. You only have 24 hours in a day. If you're spending your time scouring eBay for a tuba you can afford, or doing your own repairs because there's no budget for it, then you're not spending that time in lesson planning or score study. At my first job the budget was so pitiful I could never afford enough quality new instruments for the number of kids I had. I spent so much time finding deals on used horns, driving hours to pick up things I bought at school surplus auctions, etc.
Support from top to bottom can make or break a program. Most of the top programs out there have great instruction from kindergarten on up. They have administration who support elementary music as a class, not just a babysitting time so the "real teachers" can get some planning time (sadly, that's something I've heard). Their middle schools work with the band directors to schedule the kids into like-instrument classes at the beginner level. They don't make kids drop band for remedial test-prep classes. They find ways to let the top academic kids stay in band without it hurting their GPA. There are so many ways that administration can either help or harm the band, depending on where their priorities are and how much they're willing to adapt to make it work.
An important factor you didn't mention is parents. Another thing that most great programs have in common is support and funding from the parents. Parents who recognize the benefit of band, and will actually make the kids follow through on their commitment when it gets tough. Parents who attend concerts. Parents who make sure their kids are at rehearsal on time, and pick them up in a timely manner afterward. Parents who can volunteer their time to help with uniforms, organize meals on game day, build props, chaperone buses, move pit equipment, and do all the logistical things that make the band run. Parents who have enough money to buy their kid a good instrument and keep it in good repair, and get the kid private lessons. Parents who teach their kids the importance of hard work and dedication, and insist that they practice. Parents who can supplement the band budget, through fundraising or just higher band fees, so the band can afford the things they want to do. This is where you can have a HUGE difference even between different schools in the same district. The school in the ritzy part of town gets the same budget as the school on the wrong side of the tracks. If one school is using the budget to buy reeds and instruments for all the kids who can't afford it, and the other school is able to use that money to hire a few marching techs, which one will look better at marching contest?
Now maybe, if you're a Superman band director, you can work around all of those problems and still have a great program, win SMC, make finals at BOA. If so, you're a better teacher than I.
One more very important thing:
Don't judge an entire program based on how good their marching show is. Don't make it your only focus. As someone else said, if all you want to do is marching band, go work with a DCI group. It's entirely possible to have an unremarkable marching program (or none at all), but still have a great band program that makes great music and trains great kids. They may never see the inside of the Alamodome or Lucas Oil Stadium. If they graduate as excellent humans, they enjoyed their high school band experience, and learned the life skills that we teach in band, then that's a successful band program. High-power marching band is great, but it's not the only way to have a great band program.