At least in the case of AWS Lambda, allocating more memory to your functions can result in a faster start-up time. Just as running larger EC2 instances affords you more CPU power, so too does allocating more memory to your Lambda functions. Allocating more memory to your functions may improve performance, but note that this will affect your billing as Lambda functions are billed by the combination of execution duration and allocated memory.
You can read about CPU allocation relating to AWS Lambda in the following document: https://docs.aws.amazon.com/lambda/latest/dg/resource-model.html.
