Kerberos is required if you are going to use certain features like SQL Server Reporting Services, Outlook Web Access, Performance Point, etc where the user's request to SharePoint has to be be forwarded to a subsequent system; a process known as "the double hop".
If the system is set for Kerberos it will fall back to NTLM if Kerberos cannot be used.
To answer your question, why would you select NTLM versus Kerberos? I have seen some diabolical issues when the various apps are not setup perfectly. I have seen experienced IT people super stressed out over it. If you don't have somebody qualified to do it, and you don't have the requirements for it, then I would select NTLM.
On a separate note, relevant to your environment, I have recently heard of a documented issue involving Kerberos with Claims Auth, but I have not gotten all of the specifics yet as to the scenario.