INNER JOIN between 2 tables vs WHERE on one table performance
The second query. But why are you comparing them? 

They may return the same data but they are answering two different questions. The first retrieves all records from doctors where a record exists in clinic with id=1. The second retrieves all records from doctors with clinic_id=1 regardless of whether a record exists in clinic. 

In the absence of a foreign key constraint between the two tables, the queries are not comparable.