The verdict
If you sell software, subscriptions or downloads to customers around the world, I'd pick Lemon Squeezy. If you run an agency, consultancy or IT services firm and want to know whether a client is profitable, I'd pick Productive.
If you do both, for example an agency with a small software product, they can sit side by side because they do not overlap. Productive is not a checkout, and Lemon Squeezy has no project budgets or timesheets. I would not buy Productive for a team that only needs a task tracker. Read what Stripe's ownership means for Lemon Squeezy before you build on it.