IMHO high end gear is definitely better than good mid-range gear, but not necessarily all that important.
Low end gear is usually quite inferior.
One of the greatest sax players of the 20th century, Charlie Parker had an unfortunate heroin problem. That meant his saxophones were often in pawn shops, so he borrowed horns to play gigs and make records. Whether he was playing a top of the line horn, a student horn, or even a plastic sax (grafton), he always sounded like Charlie Parker
I have a Gibson ES-330 and an Epiphone Casino. Almost identical guitars. They both feel good in my hands and play equally as well. The Gibson costs at least 4 times as much as the Epiphone. Why the difference? Made in the USA, better wood, real MOP inlays, Gibson headstock and other 'luxury' features.
The Epiphone has aftermarket (Duncan) pickups. Unplugged, the GIbson with better wood sounds better (hollow body archtop electric). Plugged in, the Epiphone actually sounds better. Pickups are more important to the sound of the guitar than the wood.
On the other hand, my Parker DF fits me so well and has such a delightful variety of tone options, I hardly even touch the Gibson or Epiphone anymore. In fact, I've had the Parker for over a year now, and it has cured my GAS except for another Parker so I can have 2. Plus, the DF is the mid-priced Parker.
And Jimmy Page demonstrated that he can play a Danelectro better than I can play any guitar ever built.
So how important is a high-end guitar? Depends. Not even a fraction as important as your talent and technique but like driving a Lexus instead of the Camry with the same body, it feels better and can do a few additional things but they will both get you to the same place.