Yes, heat lost and heat gained are equal to each other, but the temperature that the change in temperature are different.
Look, heat exchange = m*C*temperature change.
Where m is mass and C is specific heat.
If m are the same
You can write
heat gained by metal 1 = C of metal 1 * temperature increase
heat lost by metal 2 = C of metal 2 * temperature decrease
So, C of metal 1 * temperature increase = C of metal 2 * temperature decrease.
Then the metal with the lower C will experience a bigger change of temperature.
Please, let me know if this helped you.