While we might suggest or showcase certain 3rd party drivers that can meet certain needs, we typically do not go as far as to recommend one over another as it really depends on what your needs are and if the driver meet those needs.
What I can share with you from working with the jTDS driver in past scenarios is that the latest version, 1.3.1, which you’re using, is no longer being developed by that team through SourceForge as of 2008. That specific version officially only supports up to SQL Server version 2012.
For SQL Server, have you considered using a JDBC driver from Microsoft? You can find their options at Download - JDBC Driver for SQL Server | Microsoft Docs.
For Sybase, they have some JDBC suggestions at SyBooks Online as well.