Broken down to the absolute endgame, Marxists want a stateless, classless society. Anarchists want that too, so ostensibly the goals are the same.
However, the areas of contention usually come down to these:
1. Anarchists do not believe the ends justify the means; rather, we understand that anti-authoritarian goals require anti-authoritarian means;
2. Anarchists do not believe that taking control of a state mechanism/government is compatible with anarchist goals and methods (see #1);
3. Anarchists do not believe that any coercive mechanisms (law, police, courts, prisons) are compatible with anarchist goals;
4. Anarchists do not necessarily believe that expropriating the means of production from the owning/ruling class will make other forms of exploitation and oppression disappear;
5. Anarchists do not necessarily believe that economic relations are the primary location of class tension;
6. Anarchists do not believe that centralizing decision-making and organizations is a good strategy for achieving our goals;
7. Anarchists do not believe that some kind of new consciousness is required for working class, poor, and otherwise oppressed people to take control over their own lives.
That's on the theoretical/philosophical level. In the actual history of the interactions between Marxists and anarchists, the initial split during the First International created a schism that was never resolved. Those issues helped to create the conditions for the physical (armed and lethal) confrontations throughout history: Marxists fighting anarchists in the Mexican Revolution (1910-1920), the Russian Revolution (1917-1921), and most infamously, the Spanish Revolution (1936-1937).
Marxists have also been involved in suppressing non-anarchist revolutionary moments: China (1921-1927), Russia (1919-1924), Germany (1918-1919), Vietnam (1945-1968), Spain (1936-1939), France (1945-1947), East Germany (1953), Hungary (1956), Poland (1971), Czechoslovakia (1968), Nepal (2011).
One of the most basic problems is that Marxists have one plan and one formula for their kind of revolution, and any action that is not controlled by them or that doesn't fit inside those plans and formulas are objectively counter-revolutionary - and therefore to be liquidated. Anarchists are supposed to be more flexible.