I can believe that despite its size and weight a large airliner would respond precisely to commands, but does the concept "flying by the seat of the pants" apply to such an aircraft?
The phrase "flying by the seat of the pants" is an imprecise term, and I don't have an answer for that. However, if you allow it to mean operating an aircraft in the absence of instrumentation or other capability that is normally used, or using techniques not normally used, whether you're forced to because of failure(s) or because you prefer not to use them, then here is an observation.
In the early 1990s I was flying 747-100/200 freighters. The carrier had a contract with Japan Air Lines to haul freight between Tokyo Narita and KJFK, with a crew change and refueling at Anchorage. We used a JAL call sign. JAL had their own 747-200 freighters on the route as well, more of them than our small number of aircraft. Many of their flights would have an American flight engineer who would handle the radio going into U.S. airports. Thus, the Anchorage controllers could not tell from the radio communication whether the flight had American or Japanese pilots.
One summer Anchorage took the ILS down for extended maintenance. One severe clear day during this period we were on our descent but still well out when Anchorage approach cleared us for a VOR approach. We immediately called the airport in sight and requested a visual approach, which was granted.
Curious, when we were down I called approach control on a land line and asked why we were first assigned a VOR approach. They explained that, believing our flight probably had Japanese pilots, and having had those pilots always refuse the offer of a visual approach and request a VOR approach (in spite of the additional 10 minutes of flying), approach control had simply assigned the VOR approach.
As part of our contract, we occasionally had a Japanese check captain observe us, and the next time this happened, I brought up the subject with him. He explained that their pilots were never taught to simply look at a runway and land without reference to navigational instruments, and, lacking a robust general aviation segment, their pilots simply never had experience with doing that. He added that from their standpoint, we were a bunch of cowboys. Not the exact "flying by the seat of the pants" wording, but the same sentiment.
Obviously experience and training will build up a great deal of intuition (visual, vestibular, etc) - what sort of bodily connection does an airline pilot experience with the aircraft? Is it markedly different from that of the pilot of a small plane?
When you're flying the same airplane type day in and day out, you internalize what that aircraft can do and how it will respond. You get used to its noises and even to its vibrations if you will. And regardless of how small or how large it is, it becomes the right size, neither little nor big, especially once you're in the air. When you change airplanes, and especially if it involves a significant change in size, there is a difference.
For example, I spent the last 10 years of my career on 747-100/200 aircraft. Fifteen years after retiring, and not having been in a cockpit during that time, I went out to a local airport to check out in a Cessna 172. I knew I would have trouble with flaring too high, and I warned the instructor. My first landing was a real lesson, actually to both of us. When I said to him, "I think I should flare," he said, "you're way to high." When I said, "I've got to flare,: he said, "still too high." When I said, "I'm flaring," with the sense that if I didn't I would prang the airplane, he said, "you're still a little high, but go ahead." It took me 5 hours to check out in the airplane, most of that time for landings.
