I'd say the Beatles' chord progressions were significantly more complex than most of Matthews'. Stuff like "I Am the Walrus" is insane. Then again, you're probably referring to their British Invasion material, but even then, stuff like "I'll Be Back" and "No Reply" contains some rather unconventional key changes. Then again it's been awhile since I've tried to play any of Matthews' stuff so it very well could be more complex than I'm remembering.