There are a few pieces to this answer:
1) Define Productive: Unless you are in a factory getting parts out the door, productive is a fairly vague term. Be careful that people aren't looking at busy-ness as a stand-in for effective or productive teams. Henrik Kneiberg's "Utilization Trap" video illustrates this beautifully.
2) Cross-functional teams: Are you able to make two independent cross-functional teams. A good way to measure this is to first write down all of the skills needed to deliver a feature (or whatever your team is delivering). Then have each person rank themselves in each of those skills on a scale something like this: 0-no skill; 1- beginner; 2-check my work; 3-professional (independent work); 4-master/mentor. Now, can you build 2 independent teams with all of the skills represented with at least a 3? If not, that is a non-starter.
3) Experiment: Assuming you can create 2 cross-functional independent teams, then you're left with the hard reality that the only way to know if it will be better is to try it. Design an experiment to find out. Make sure your constraints don't artificially hamper one setup and that the results are objectively measured in a way that shows what your organization wants out of productivity. Then run both ways for a few sprints and see what works better.