Having owned both Gibson and Fender electrics (Les Paul, Strat and Telecaster), and played many more of them over the years, I would submit that they are very different instruments. The methods of construction are different (different woods, different weights, "set in" vs. "bolt on" necks), the scale lengths are different (Fender is 25.5 inches, Gibson is 24.75 inches), the necks feel very different, the electronics are different, etc., etc. Anyone who has spent a significant amount of time playing both would attest to the different "feel" of the instruments, and the different sounds they produce. Moreover, within the two companies you have a wide array of choices -- pickup types (single or double coil, high gain vs. "polite," coil taps, in or out of phase, etc.)and configurations, various types of whammy bar vs. stop tailpiece vs. string-through vs. floating bridge, etc. Myriad choices, which can make a profound difference on the sound.

It is also true that what you are playing through can be as important as what guitar you are playing. The type of amplification (tube class A, tube class A/B, solid state, modeling amplifiers, size and number of speakers, cabinet dimensions, wattage, etc.) makes a huge difference, as does the number and type of effects, the pre and post gain levels, and so on. This is not even close to a thorough exploration of the variables, and how they interact with one another -- merely a list of a few of the factors that shape the sound. Some types of setups mask the "true" tone of the guitar more than others, and with heavy overdrive and/or effects you may in fact have trouble telling what guitar is being played. But if you take a stock Strat into a stock Fender Twin on a relatively clean setting, and then compare it to a stock Les Paul Standard through the same amp at the same settings, I think most will hear the difference pretty quickly.

Of course, the player is the biggest variable of all. Some players do their best on Fenders, some on Gibsons, some on other brands (my current main electric guitar is a PRS, which is a different beast altogether). Many players have more than one electric guitar, and switch off for different tones.

For the record, there have been many "Lucilles" over the years; mostly Gibsons, but early on B.B. could be seen playing a Telecaster, and in the very early days he had a variety of other (lesser) instruments. The "Lucille" model that Gibson came out with in 1979 or thereabouts resembled an ES-335 (a dual-cutaway semi-hollow body with two humbucking pickups), but as someone mentioned it had no F-holes, and it also had an adjustable stop tailpiece rather than the stock stop tailpiece found on most 335's, as well as some cosmetic differences. For the most part Muddy played stock Telecasters, although you can see him with various other instruments in pictures from the 40's and 50's.