Sometimes two products are there to stay - just ask BlueYonder, SAP, Korber or plenty of other large enterprise software vendors which end up with two products (be it merchandising systems, ERPs or WMS products they have ended up with via acquisition).
That's true, though more often the case with products that have a lot of overlap, versus really being competitors in the same market. Perhaps Trello is a good example. It overlaps with Jira, but it doesn't really compete for the exact same customers in an either/or decision.
It's hard to find a good example where a merger of two products with very similar markets where both products thrived after the merger.
