Ron,
I believe that your true question is "Why do not experienced planetary observers using larger instruments detect more detail over the planets." This actually depends upon many factors such as the quality of the lens or mirror (larger objectives are more difficult to figure to a diffraction-limited surface), structure enclosing the instrument (older observatories used material (e.g. steel) which held heat too readily and were poorly ventilated compared to modern (open) observatories), experience of the observer (a factor not mentioned enough), and most importantly the steadiness of our atmosphere (or seeing conditions).
The observation of Saturn made by the famous planetary astronomer Edward Emerson Barnard you refer to (on the right in the attached image) was made on July 2, 1894. Barnard was using the famous 36" Lick refractor at the time to make his observation. Since the Lick refractor was first pressed into service in 1888, ironically the other attached image made by James Keeler was practically the maiden observation using this fine instrument, Barnard had enjoyed many fine views of the Moon and planets which superseded any other made before that time. He wrote of this observation of Saturn "It is true that the picture appears abnormally devoid of details when compared with drawings made with some of the smaller telescopes. I am satisfied, however, to let it remain so." Barnard was, honestly, recording only the features that were held steadily throughout his observation as any observer should do. I understand this statement as I myself have observed details over the planets that were not consistently visible and therefore not recorded in the final drawing. One must remember that the planet Saturn presents very low contrast features over it's globe and not even orbiting instruments (HST) record much more detail over the ringed planet.
James E. Keeler, the first staff astronomer of the Lick Observatory and a pioneer in astrophysics, made his observation of Saturn on January 7, 1888. Keeler was using an impressive magnification of 1,000x on the giant refractor (what a view that must have been!). He stated upon placing Saturn in the field of view "beyond doubt the greatest telescopic spectacle ever beheld by man. The giant planet with its wonderful rings, its belts, its satellites, shone with a splendor and distinctness of detail never before equalled." Keeler discovered a faint gap in the outer portion of ring A during that observation now know as the Keeler division (not to be confused with the Encke division or gap which are closer to the center of ring A).
The point of the above observations is to show that if given the proper atmospheric (seeing) conditions then an experienced observer will detect features over a planetary surface or atmosphere that a smaller instrument will fail to detect. This is not a condemnation of smaller instruments used on the planets but only a fact that a larger aperture instrument (assuming a well-figured objective) will ( by reason of increased resolution) detect finer details upon a planetary surface or atmosphere if the atmospheric (seeing) conditions permit. The smaller instrument, in general, will be useful on many more observing sessions if the seeing conditions at a specific site are average (5/10) at best. That is why we, using our smaller instruments (e.g. 4-10 inches aperture) will "see" more detail upon the planets, in general, than larger instruments as the average air cell is approximately 10 inches (25 cm) in diameter.