The contract should clearly spell out who owns the IP. As a startup...you want to own the IP of course. Make sure your lawyers check the IP clauses
Even if you have them own some part of the data, make sure you’re granted a “perpetual, royalty free, worldwide, irrevocable license” to use the data for the improvement of your services. Definitely want your attorney involved
Lots of companies will try to own anything you customize by default, but that can really harm the startup for future financing and M&A (and future customers may not want to buy your product if you don't have clear IP rights to it)
As long as the contract is clear that you own yours + improvements, and they own theirs + improvements, agreed - the closer the two businesses are in terms of product, the harder it will be to draw a line.