There can be some latency differences between the different database APIs but it is nowhere near 100ms for the equivalent payload.
As pointed out in the comments, your assumption about the Core API is incorrect. Core API itself underlies all the other API's which sit atop of it.
Core API is the only one that provides an SLA on latency. This is guaranteed to be less than 10ms for in-region reads and writes at P99 when the payload is 1KB or less and using either .NET or Java SDK via Direct TCP mode (the default).
All other database APIs go through a gateway (as does Core API Python and Node.js SDKs). Also queries are executed on the gateway due to the fact they may talk to different partitions. Gateway also creates query plans and otherwise coordinates query execution.
Bottom line, Cosmos DB is fast across all its database APIs. But if you are trying to squeeze out every ms of latency, use Core API and either the Cosmos DB .NET or Java SDK's.