I can't speak to the Roku TV. But your Roku 3 is old, very old. There are two versions of the 3, the model 4200 released in March 2013 and the 4230 released in April 2015. So yours is either more than ten years or more than 8. Either way Roku has made massive improvements in the hardware used in their players. Both of these models are still officially supported by Roku, but I honestly don't expect that to continue a whole lot longer. They've already stopped supporting some newer players.
The Roku 3 (either version) was an outstanding player for their time. But they simply can't keep up with some of the latest channels/apps offered by providers. I saw similar performance issues with my old 2 XS as it aged as well, so that is the most likely culprit of your problem. The solution is to replace your Roku 3 with an Express 4K+. You would be amazed at the improvements in performance compared to your 3.
Again, I can't speak to your TV. Until this year, Roku themselves did not build the TVs so the manufacturers might not have used the best hardware to run their TVs. Depending on the brand and model of your TV, it could be getting up in age as well.
Roku Community Streaming Expert
Help others find this answer and click "Accept as Solution." If you appreciate my answer, maybe give me a Kudo.