Though in different keys, "Good Vibrations" (in E-flat) and "I'll Be Back" (in A) feature the same chord progression: i - bVII - bVI - V. They therefore serve as the perfect comparison, showing what Paul played and what the Beach Boys played given the exact same chord progression.
In "I'll Be Back", Paul plays the root (scale degree 1) of each chord almost exclusively (occasionally he'll play the fifth instead). The Beach Boys play a more melodic pattern using scale degrees 1, 2, 3, and 5. McCartney also plays in very bottom of the bass's range, whereas the Beach Boys played in the upper register, giving it a very different timbre.
Now here are a few MIDI excerpts, both transposed to the same key (C), for side-by-side comparison: first is the opening phrase of "Good Vibrations"; next the opening phrase of "I'll Be Back". And since the tunes use identical chord progressions, we can substitute one bass line for the other to further compare them: here is "Good Vibrations" with Paul's bass line from "I'll Be Back"; and here is "I'll Be Back" with the Beach Boys' bass line from "Good Vibrations". By comparing these 4 excerpts side by side, we can easily hear how much more melodic and sophisticated the Beach Boys' bass line is than the Beatles'. Paul, of course, could hear it, too - and he responded by making his own bass playing more melodic.