Both updates include tons of bug fixes. Here are some highlights of what issues were fixed (read the release notes for a full list):
vCenter Server 5.1 Update 1
- False alarms reported for VMs (KB2009783)
- Unable to clone a vApp on a Datastore cluster
- Performance stats for last year shows only one month (KB2042009)
- Login to Web Client fails with non-ASCII characters in username
- Advanced performance charts display very slowly in Web Client
- Logging into vCenter Server using the vSphere Client with vCenter Single Sign-On (SSO) in a multi-domain environment fails (KB2037410)
- vSphere Client stops responding when Virtual Machines are hidden from view (KB2016224)
- Unable to vMotion a VM that is connected to a vDS without uplinks (KB1003832)
- Storage vMotion does not rename VM files (KB2008877)
ESXi 5.1 Update 1
- ESXi host UUID field byte orders were not reported as per SMBIOS version 2.6 (this resulted in "VM was moved or copied" messages after upgrading a host from ESXi 4.x).
- SNMP trap files fill up root inode tables, resulting in host disconnection (KB2040707)
- Virtual machines become unresponsive with busy vCPUs on ESXi 5.1 (KB2045154)
- Multiple vMotion interfaces and long running vMotion(s) result in unicast flooding (KB2000119)
- ESXi 5.1 host fails with a purple diagnostic screen when Beacon probing is enabled (KB2038281)
- If a quiesced snapshot fails redo logs are not consolidated
- Lots of VMware Tools issues were fixed.
Please note that a lot of these issues have already been fixed for vSphere 5.0 with 5.0 Update 2, and these fixes have now been ported to vSphere 5.1 with 5.1 Update 1.