Multiplication vs exponentiation in pairing based cryptography $$P\in G_1$$$$Q\in G_1$$          $$a,b \in Z_q$$         $G_1$ isadditive cyclic group of prime order $q$
$$e(P^{a+b},Q)------(1)$$
$$e(aP+bP,Q)----(2)$$
(1) and (2) will give the same pairing result $e(P,Q)^{a+b}$.
In (1) and (2), despite of same pairing result, is there difference in terms of security or performance for different operations (exponentiation, multiplication and addition) in $P$?In (1), I don't know clearly about exponentiation is allowed or not with randomly generated $P$ value from additive group.
The problem is that you are comparing apples and oranges. A group has a single operation associated to it. Depending on your notational conventions you either need to write (1) $e((a+b)P,Q)$ and (2) $e(aP+bP,Q)$ if you write $G_1$ additively or (1) $e(P^{a+b},Q)$ and (2) $e(P^a \cdot P^b,Q)$ if you write $G_1$ multiplicatively. The cost of computing $(a+b)P$ or $aP+bP$ depends on your approach to scalar multiplication, but typically the former approach will be more efficient.