Did Marx play more of a prominent role in the development of communist theory?

Yeah, this is basically it. Engels is a 'founding father' and one of the leading communist theorists, but the entire backbone of modern communism is built upon Marx's discoveries. Engels himself thought as much:

These two great discoveries, the materialistic conception of history and the revelation of the secret of capitalistic production through surplus-value, we owe to Marx. With these discoveries, Socialism became a science. The next thing was to work out all its details and relations.

(from Engels' "Socialism: Utopian And Scientific", 1880)

The basic thought running through the Manifesto — that economic production, and the structure of society of every historical epoch necessarily arising therefrom, constitute the foundation for the political and intellectual history of that epoch; that consequently (ever since the dissolution of the primaeval communal ownership of land) all history has been a history of class struggles, of struggles between exploited and exploiting, between dominated and dominating classes at various stages of social evolution; that this struggle, however, has now reached a stage where the exploited and oppressed class (the proletariat) can no longer emancipate itself from the class which exploits and oppresses it (the bourgeoisie), without at the same time forever freeing the whole of society from exploitation, oppression, class struggles — this basic thought belongs solely and exclusively to Marx.

(from Engels' 1883 introduction to the German edition of The Communist Manifesto)

You can find similar sentiments in other writings by Engels.

edit: Here's an article about Marx's death in 1883 which includes other socialist accounts of Marx's overwhelming importance. https://www.marxists.org/archive/marx/works/1883/death/dersoz1.htm

The Paris branch of the French Workers' Party expresses its grief at the loss of the thinker whose materialist conception of history and analysis of capitalist production founded scientific socialism and the present revolutionary communist movement.

and from Willhelm Liebknecht:

The science of society that Marx revealed to the people kills capitalism, and with it the idols and masters of the earth who will not let God die as long as they live. Science is not German. It knows no barriers, and least of all the barriers of nationality It was therefore natural that the creator of Capital should also become the creator of the International Working Men's Association. The basis of science, which we owe to Marx, puts us in a position to resist all attacks of the enemy and to continue with ever-increasing strength the fight which we have undertaken. Marx changed the Social-Democracy from a sect, a school, into a party, the party which is now fighting undaunted and which will be victorious.