Cartridges were probably pretty fast to load, but I don't expect that Commodore's floppy drives were particularly fast, even if they were much faster than cassette tape.
Both atari 8 bit and commodore had a disk drive with a trimmed down 6502 in it so you basically bought a second computer. This is why the drives cost more than the computer itself.
So the atari was relatively fast! I never knew. I didn't have the disk drive until I was much older.