As usual with such benchmarks, I miss performance comparisons over time. Did Fargate outperform the other two solutions because it's generally faster or because API Gateway was just slow during the few minutes that benchmark took?

What'd also be interesting here would be a price comparison. Without having done the math I'd expect Fargate to be significantly more expensive than the other solutions, which'd make a nice trade-off of cost vs. performance: If performance matters choose Fargate, if cost matters choose API Gateway as service proxy.