The future is only ESXi
With the new release of vSphere 4.1 there are some changes and news:
the terminology as changed and now ESXi is ESXi Hypervisor Architecture
the "old" ESX (or full ESX or legacy ESX or ESX with the service console) is available in the last release, from next version ONLY ESXi will be available.
VMware suggest to migrate to ESXi, the preferred hypervisor architecture from VMware. ESXi is recommended for all deployments of the new vSphere 4.1 release. For planning purposes, it is important to know that vSphere 4.1 is the last vSphere release to support both ESX and ESXi hypervisor architectures; all future releases of vSphere will only support the ESXi architecture.
On how to migrate see: http://www.vmware.com/products/vsphere/esxi-and-esx/
ESX vs ESXi
ESX and ESXi official comparison:
http://kb.vmware.com/kb/1006543 - VMware ESX and ESXi 3.5 Comparison
http://kb.vmware.com/kb/1015000 - VMware ESX and ESXi 4.0 Comparison
Probably the big difference is that ESXi has a POSIX Management Appliance that runs within the vmkernel and ESX has a GNU/Linux Management Appliance that runs within a VM.
ESX vs. ESXi which is better?
ESXi vs. ESX: A comparison of features
Note that HCL can be differed from ESX and ESXi:
No official interactive console (there is only a "unsupported" hidden console: http://www.virtualizationadmin.com/articles-tutorials/vmware-esx-articles/general/how-to-access-the-vmware-esxi-hidden-console.html) - With 4.1 the Tech mode support is now fully supported
ESXi 4.0 has no official supported SSH access (there is only a "unsupported" access: http://www.yellow-bricks.com/2008/08/10/howto-esxi-and-ssh/) - Changed in 4.1, where SSH is a service
No /etc/ssh/sshd_config file for SSH non-root access (but is still possible: http://www.yellow-bricks.com/2008/08/14/esxi-ssh-and-non-root-users/)
No support for some 3th part backup programs (see also Backup solutions for VMware ESXi) - Resolved with "last" version of those programs
No support for some 3th part programs
ESXi 4.0 hasn't Active Directory authentication for "local" user - Implemented in 4.1
No full crontab for schedule jobs and scripts locally (but there is a root crontab in /var/spool/cron/crontabs/root)
No hot-add feature for virtual disk in ESXi 4.0, but only on ESXi 3.5 (or also on ESXi Advanced with hot-add license) - resolved with first updates
No SNMP "get" polling"
No virtual Serial or Parallel port
No USB disk in the "console"
No support for mount ext2/ext3/ntfs/cifs filesystem in the console
No fully functional esxtop
No fully functional esxcfg-mpath
No vscsiStats tool
ESXi 4.0 has only experimental support for boot from SAN - Resolved with 4.1
ESXi 4.0 has limited PXE install or scriptable installation (but seems that there is a solution: http://www.vmware.com/pdf/vsp_4_pxe_boot_esxi.pdf and http://www.mikedipetrillo.com/mikedvirtualization/2008/11/howto-pxe-boot-esxi.html) - Resolved with ESXi 4.1
Normally with a standalone ESXi host you'll get 1 hour of performance data, the graph should be set to reset every 20 seconds (you can also extend the performance data to 36 hours will a simple hack - http://www.vm-help.com/esx/esx3i/extending_performance_data.php)
Free ESXi (or VMware vSphere Hypervisor 4.1) limitations
ESXi 4.x free can not be connected to a vCenter Center (it required a VC agent license)
VCB does not work (it require a VCB license)
Lot of 3th part backup programs does not work with free ESXi (see also: Backup solutions for VMware ESXi)
RCLI and VMware Infrastructure toolkit are limited to read-only access for ESXi free
Free ESXi does not support SNMP
Free ESXi does not support Active Directory integration at this time
Free ESXi does not support Jumbo Frame - http://kb.vmware.com/kb/1012454
Free ESXi EULA has some interesting restrictions including enforced read only mode for v4 and later versions of v3.5.
See also: What's the difference between free ESXi and licensed ESXi?
VMware ESX/ESXi EULA - http://www.vmware.com/download/eula/esx_esxi_eula.html
Fast to install / reinstall
Can be installed on a SD flash card or USB key (there is also an embedded version that is pre-installed) - ESXi installation - Flash memory vs Hard disk
Easy to configure (there is a simple configuration menu)
Small footprint = fast and easy to patch + (maybe) more secure
Extremely thin = fast installation + faster boot
Does not use a vmdk for console filesystems (as ESX 4.0 does)
There is a tool for dump ESXi configuration
Near to be "plug and play" (for example with the embedded version and the Host Profile feature)