Depends on their algorithm. Since you didn't specify that robots were perfect in any way or had defense mechanisms to counteract their attack mechanisms, they can easily end up attacking each other with things they can't defend against. Which is going to end up being the case with anything other than a 100% perfect algorithm, which might as well be God or very simple robots.
And considering such a situation, the one that would win... well again, depends on algorithm. They may have a slow-burn ability (to talk in gaming terms, damage over time attack) that once used, will end up killing both robots. Even instant attacks might be slow enough to both be used before they're both destroyed.
So most likely, the robots would end up destroying each other with the same attack. There is an unlikely case of the robots having attacks that hit fast enough to not allow retribution (think >= speed of light), there the winner could be the one that attacked first, but I imagine you're talking the ideal case (even though impossible without divine intervention) of starting at the same time. Also, if they don't attack at the same time, their algorithms may not execute in the same order, which would again lead to winner by algorithm (even if it's the same one, the if clauses could execute differently).
So to sum up, neither/both unless different start and/or near-instant death blows. Unless RNG ofc, but that in play, it's anyone's guess and depends on how the RNG system is implemented.