I suggest doing it in two steps:
# set fixed value to 'c2' where the condition is met
df.loc[df['c1'] == 'Value', 'c2'] = 10
# copy value from 'c3' to 'c2' where the condition is NOT met
df.loc[df['c1'] != 'Value', 'c2'] = df[df['c1'] != 'Value', 'c3']