Yes, we competed with SAP in a specific industry and honestly our tools were better and more user friendly, and no, they were not all huge companies, which is one of the reasons we were able to eat SAP's cake because we were much cheaper. I believe we got the job 90% of the time when we were shortlisted with SAP.
We lost some customers to SAP later on because they become bigger and "consultants" told them that they should switch to SAP because, you know, all big companies use SAP. I haven't heard of any success stories from those customers yet (this is not entirely SAP's fault though).