My experience with "big glass" is that these expensive lenses offer excellent sharpness, even at wide apertures like wide-open, and stopped down 2/3 of a stop to 1 stop, offer truly biting image sharpness. The issue with smaller lenses, like Canon's 400mm f/5.6 or Nikon's older 400mm f/5.6 Ai-S is that the f/5.6 aperture often leads to slower shutter speeds than would an f/2.8 or f/3.5 400mm lens, and the difference in sharpness between say 1/500 second and 1/2000 second is often quite a bit. Really FAST shutter speeds FREEZE subject movement, and prevent camera shake blurring...the lightest bit of camera movement at say 1/500 or 1/750 second at f/5.6 can make shots less-crisp than if the shutter speed were higher, like 1/1000 or 1/1250 or 1/1500 or even 1/2000 or 1/2500.
The second issue is price vs quality: my experience is that yes, the $4,000-$7995 big glass lenses (Nikons) are sharper than lower-spec'd lenses...you cannot compare lenses like a 200/2 or a 300/2.,8 or a 400/2.8, a "super-telephoto prime", with consumer-level lenses.
One issue too is often overlooked: diffraction. As we've gotten into high-megapixel sensor, the sharpness-robbing effects of diffraction mean that at apertures as small as f/4, diffraction can actually limit sharpness, and at f/5.6 or f/6.3, a 24-MP or 36-MP or 42-MP sensor will make an image that is a little bit less crisp that if the image had been made at say, f/3.2. I noticed this years ago, on the Nikon D2x, when we got to 12 MP, and I see it now more often...WIDER f/stop openings, physically WIDER HOLES, let light in, without diffracting the light through a tiny-sized hole...I was surprised to see that on 12MP DX, diffraction started cutting my sharpness from the 70-200/2.8 VR-G lens at f/4.5....f/4.2 was actually noticeable sharper than was f/5.6!!! With prime lenses, the 200/2 VR-G was sharper at f/2.5 than it was at f/5.6...
Greater depth of field can tend to mask the effect of diffraction...but...on a single-plane subject, if the lens is truly excellent optically, you'll get a better,crisper image at wider f/stops than you will at f/5.6. There's a reason that 400/2.8 lenses exist. They have their purpose. if you can get a shot at ISO 250 at f/3.2 at 1/2000 second, as opposed to being stuck way slower at f/5.6, the results can show the difference in both ISO level shot at, and/or slowness of shutter speed.
Diffraction is based on physical width of the light-admitting hole...not on the numerical f/value...this is an issue many people are unfamiliar with. With a big, long lens design, like on a 400mm f/2.8, there is a wide-aperture range where there will be basically, almost no noticeable diffraction. When the lens designers set out to make a $10,000 lens...they can hand-culture the front element glass, and use rare-earth glasses, and special grinds, and the most-costly optical formulas needed to make a really,really,really high-performance lens; the same level of optical performance is not part of the design consideration with a $689-$1100 lens.