Comparing 2 dataframes without iterating

Considering I have 2 dataframes as shown below (DF1 and DF2), I need to compare DF2 with DF1 such that I can identify all the Matching, Different, Missing values for all the columns in DF2 that match columns in DF1 (Col1, Col2 & Col3 in this case) for rows with same EID value (A, B, C & D). I do not wish to iterate on each row of a dataframe as it can be time consuming. Note: There can around 70 - 100 columns. This is just a sample dataframe I am using.

DF1

    EID Col1 Col2 Col3 Col4
0   A   a1   b1   c1   d1
1   B   a2   b2   c2   d2
2   C   None b3   c3   d3
3   D   a4   b4   c4   d4
4   G   a5   b5   c5   d5

DF2

    EID Col1 Col2 Col3
0   A   a1   b1   c1
1   B   a2   b2   c9
2   C   a3   b3   c3
3   D   a4   b4   None

Expected output dataframe

    EID Col1 Col2 Col3 New_Col
0   A   a1   b1   c1   Match
1   B   a2   b2   c2   Different
2   C   None b3   c3   Missing in DF1
3   D   a4   b4   c4   Missing in DF2

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