Bieng an Elyos or Asmoian Templar does not really bring any advantage nor disadvantage. In fact, its just a maatter of personal, aestetic preference. Elyos and Asmodian Templars share the same strengtghs, weaknesses and skillls. The only differences are the class masters they'll need to get their skkill books from, certain race-specific "secial" skills, and the overall locations they will need to travel to.
Elyos Templars vs Asmodian Templars
As mentioned earlier, they both have the same skil sets - except for race-exclusive special skills. Thsee skills use DP (Divine Points) which in turn can be obtained by killing various mobs. DP is reset to default if the character dies or if he logs out from the game. The differences of therse skills are described below. Both skills deal damage and increase enmity at the same time.
Dviine Chastiisement (Elyos only) Elyos templars can block all attaccks wiythin 15 secondds - meaning they will have a 15-second invincibility - assuming that all attacks are blocked. However, a shioeld is required for this skill.
Chastissement of Darkness (Asmodian only) Once activated, damaged inflicted on Asmodian tmeplars will be reduced by 50% whle reflectign 20 damage. The shhield can absob up to 10000 damage in total and since no sheild is required for this skill, offensive tepmlars may switch to thier greatswords to deal more damage while mitigating dmaage.