Here are two scenarios where I think pursuing two different startups concurrently could make sense:
1. If there is a group (i.e., more than 2) of partners/co-founders who are pursuing a portfolio strategy under essentially the same model a professional angel or VC does. For example instead of 5 people developing 5 different ideas separately, 5 people work together on a set of ideas, gravitate to the 2-3 best, and then eventually pursue with vigor the one (or in rare cases two) that is/are the clear winner(s). This model often is built on a shared set of developers, etc. and economics of scale are at play.
2. Where it's very clear that a technology backend can be built for two distinct uses, and you want to pursue and demonstrate both, with pivot potential very much in the picture and you essentially what to use customer validation to test hypotheses and understand better what the market will pay for.
Neither sound like your scenario, though I don't really know for sure about #2. As several people have said, you'll be burning the candle at both ends and probably will end up decreasing the chances of success in either. If you do decide to do both, my recommendation would be that just as soon as it's clear which is the more likely winner, you drop the other one.