Sql-server – the different between GDR security update and CU security update

From the error messages in the summary log, it seems like the baseline MSIs could not be found (perhaps because you cleaned out C:\Windows\Installer?).

I would suggest:

1. Installing the QFE instead of the GDR (this will attempt to patch you to 10.0.6535, giving you this security fix and a couple of other fixes described here).
2. Not using Windows Update, but rather applying the patch manually. This may bypass whatever problem Windows Update is having finding the baseline MSIs, and if not, may give you better error messages interactively.
3. Investigating the log file with the KB article number in the file name, as @Ali suggested.

To understand the jargons, Aaron Bertrand has a #BackToBasics blog post

Also, refer to this decision matrix for TLS 1.2 support or MS KB - TLS 1.2 support for Microsoft SQL Server

10.50.6220 => SQL Server 2008R2 SP3 GDR

10.50.6529 => SQL Server 2008R2 SP3 QFE

From the decision matirx, if you dont want TLS 1.2 support, dont install 10.50.6542. TLS 1.2 support got introduced in 10.50.6537.

So to answer your question which one to install ... it will be 10.50.6220.

As always, test out your application behavior when installing a new fix.