Marx and Engels were collaborators, but many phrases and key Marxian terminology that are wrongly attributed to Marx were actually coined by Engels, such as the infamous phrase "dialectical materialism", particularly in his work Dialectics of Nature from 1883. (The actual term employed by Engels is materialist dialectic, dialectical materialism was later coined by the Marxist theoretician Plekhanov). The Dialectics of Nature is largely considered an outdated text which intends to apply the Hegelian dialectic to science and nature itself, often leading to pseudoscientific conclusions through Engels' attempt to extract universal scientific laws from what is now considered a heuristic logical device. After Marx's death, Engels attempted to refine and systematize Marxian thought, and Engels for many Marxian scholars was considered the first "Marxist revisionist". However, as Alvin Gouldner suggests in his book The Two Marxisms:
"The imputation of a radical gulf between Marx and Engels, heedless of the differences in the periods in which they worked, and which fails to see Marx's own movement toward science, survives less because of its intellectual justification than because of the need it serves. What is at work here is the need to deal with the real contradiction within Marxism, its Januslike character as both a Scientific Marxism and Critical Marxism. "
Thus, Gouldner proposes that people attempting to juxtapose Engels and Marx are really seeing the difference between what is recognized by contemporary Marxian scholars as the difference between early and late Marx (a difference elaborated by Marxist philosopher Louis Althusser). It should be noted that the attempt to identify all of the flaws of Scientific Marxism (the historical presupposition of unilinear evolutionism, etc) with Engels fails because all of this flowed directly from Marx's own engagement with scholars such as Lewis Henry Morgan (in addition to presuppositions present already in Hegel). Thus, while some contemporary Marxist scholars may disagree with some of the theoretical premises of Engels' The Origin of the Family, Private Property, and the State (1884), the anthropology this is based on (namely Lewis Henry Morgan) was cited often in Das Kapital, and this particularly work (considered by many Engels' most lasting contribution to Marxist theory) was based on Marx's own research notes.
However, one difference that has been suggested theoretically between Engels and Marx is this:
"Engels's view of capitalism involves a distinctive, ecologically sensitive critique of its degradation of nature. Capitalism and its social science, political economy, "concerns itself for the most part only with the immediately intended social effects of human activities directed towards production and exchange." Capitalism means a narrowing of attention to market conditions and profit-making activity, and a corresponding neglect of the effects of their actions on nature. "
I'm not sure if I personally agree with this distinction because the doctrine of alienation from nature is already present in early Marx, particularly in the Economic and PhilosophicalManuscripts of 1844. To quote from this:
" In estranging from man (1) nature, and (2) himself, his own active functions, his life activity, estranged labor estranges the species from man. It changes for him the life of the species into a means of individual life. First it estranges the life of the species and individual life, and secondly it makes individual life in its abstract form the purpose of the life of the species, likewise in its abstract and estranged form."
Engels himself had a completely different personal background than Marx. His father was the owner of a textile mill, but Marx financially struggled throughout most of his life as an editor, radical labor organizer, political activist, and author. Marx was raised in a solidly middle class home in Trier. However, despite these differences, the friendship between Engels and Marx was lifelong, lasting from 1845 with the publishing of The Condition of the Working Class in England to Marx's death in 1883. If anything, Engels can be criticized for being too faithful to Marx; however, some scholars still maintain that Engels later writings, particularly the Anti-Duhring, can be blamed for the creation of the orthodox Marxist doctrines later taken up by the Soviet Union, including dialectical materialism and scientific socialism. The difference between the two writers can be summed up by the fact that Marx was far more interested in matters of political economy and philosophy while Engels was interested in making Marxism into a political reality, but on the other hand they were both leading leftist intellectuals both versed in Hegelian philosophy and other subjects and tried together to create the political ideology known as Communism.
It should be remembered that Marx famously said "I am not a Marxist", but it should also be remembered that Engels collaborated on Marx's most famous works, including Das Kapital (Capital) and the Communist Manifesto, and shared in Marx's fundamental beliefs in social transformation through a revolution of the working class to overthrow the existing capitalist system. However, it should also be remembered that while Marx referred to individual capitalists, Marx nor Engels never referred to the existing economic system as capitalism.
Sources:
Karl Marx: The Burden of Reason (why Marx Rejected Politics and the Market) by Alan Megill
The Two Marxisms. New York: Oxford University Press, 1980, Chapter 9 - "Engels Against Marx? Marxism as Property" pp. 250-286. by Alvin Gouldner
The Origin of the Family, Private Property, and the State (1884) by Friedrich Engels
Dialectics of Nature (1883) by Friedrich Engels
Economic and Philosophical Manuscripts of 1844 by Karl Marx