After' compared ',when do we use the preposition 'with' and 'to'?

Dear Student
To compare to is to point out or imply resemblances between objects regarded as essentially of a different order;

To compare with is mainly to point out differences between objects regarded as essentially of the same order.

Example :
life has been compared to a pilgrimage, to a drama, to a battle;
Congress may be compared with the Chinese Parliament.
Rome has been compared to ancient Egypt;
Russia may be compared with modern USA.

Regards