Wouldn't Athena be the service closest to BigQuery?
Athena lets you run SQL queries on datasets in S3. You can do something similar in BQ with external tables. BQ is much faster. Athena will easily be more expensive on larger datasets, because you pay $5 per terabyte scanned.
AWS doesn't have a service similar to BQ in terms of performance.
I think the 3 main players in the Analytics space are BQ, Snowflake and Databricks.
But given that Athena uses HiveQL for DDL I'm gonna stand by my original statement.