What are/were the 1967 Impala's main competition

Just off the top of my brain I would say the Galaxy the Montego the Coronet the Roadrunner
You say compete how ? I assume you mean in "class" of car, wheel base, # of doors, performance options, "footprint" so to speak,,,,, or ?????

Mom and Dad had a 1964 Galaxy 500xl convertible. It was white with electric blue interior. I was 11yrs old riding to school in that car. I was "someone". My dad hated that car and kept it for 2 years. Bought a Skylark GS convertible after that. It too was pretty.