The OGE exam is intended for graduates from the 9th grade and is designed for the level of Pre-Intermediate language proficiency (corresponds to A2 and B1 on the CEFR scale, in the OGE there are tasks of both levels).
The EGE exam is passed by the graduates of the 11th grade, the required level of knowledge of English for its successful completion is Upper-Intermediate (there are tasks of both basic level (A2) and tasks of increased complexity (B2)). That is, approximately the level of the Cambridge FCE exam.