Lower cost. AWS usually has huge premiums over the raw EC2/S3/EFS costs.
Having used AWS Elasticsearch, it has a lot of deep problems with it in its current state so Elastic can compete on value just fine.
In other news, I think the Elastic licensing change beyond being ethically a dick move (legally it's their right), is just horrible business strategy. I said on this site several days ago that Amazon was just going to make an Apache 2.0 fork and keep chugging along, and that's exactly what we're seeing.
Your margin is my opportunity. (c)
Though AWS still growing too fast atm so they value quantity of services over quality. But once they have capacity they can squeeze out of business almost anyone.