The amount of cross product backend code reuse is going to be staggering. Nothing I enjoy more than vanilla packaged with 50 different names.
Having been part of quite a few mergers over the years, I would say that these 2 products will never ever merge the codebase. In fact, in a few years when they say it's a single product, there is a 99% chance they still exist as totally separate codebases. Many products these days are multiple products disguised under a single trench coat.
Honestly getting them to use the same login across both platforms will probably take a year to finish.
Financing the cost of the merger may lead to higher prices.Less competition may lead to higher prices.