Are vaishnavism patha and shaivism patha leads to same parmatman / GOD ?
Yes, both leads to same parmatman.
त्रयी साङ्ख्यं योगः पशुपतिमतं वैष्णवमिति
प्रभिन्ने प्रस्थाने परमिदमदः पथ्यमिति च।
रुचीनां वैचित्र्यादृजुकुटिल नानापथजुषां
नृणामेको गम्यस्त्वमसि पयसामर्णव इव॥ ७॥
The different practices based on the three Vedas, SaMkhya, Yoga, Pashupata-mata, VaishhNava-mata etc . are but different paths (to reach to the Greatest Truth) and people on account of their different aptitude choose from them whatever they think best and deserved to be accepted . But as the sea is the final resting place for all types of streams , You are the only reaching place for all people whichever path,straight or zigzag, they may accept .
From Mahimna Strotra