Solution 1:

You can use Cloud Trace to measure every request that your Functions make or receive; with Cloud Trace you can see a detailed view of how many milliseconds takes to complete certain requests.

You can also integrate with Cloud Logging to gather more details, like the agent that made the request to see for example, maybe the requests take more in Mozilla than Chrome.

Here is a guide that could help you set up and use Trace to compare response times.