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Based on power consumption, system performance, support and quality of manufacturing. Results are based on my personal opinion derived from lab testing database response times for clients.
Installed Options:
Two (2) Dual Core Processors
4GB RAM
Gigabit Ethernet
#1 Sun Fire X4100
AMD Dual-Core Opteron 2.6Ghz
Cost, performance, lowest power consumption in the industry and (my favorite) lower fan noise
#2 IBM eServer 326m
AMD Dual Core Opteron 2.60GHz
HP ProLiant DL360 G4p
Intel Xeon ( FOUR INTERNAL DRIVES)
Dell PowerEdge 1850 (good price)
Dual Core Intel Xeon 2.8GHz
HP ProLiant DL140/DL145 (good price)
Intel Xeon or AMD Opteron
Unfortunately, your best option for dual processors at a reasonably low power is hard to find in 1U form, at least pre-built.
The "consumer"-oriented AMD Athlon X2 chips (Socket 939 and now AM2) are a better proposition power-wise than the Opterons. The Opterons, on the other hand, are better-suited for servers. It's actually difficult to find a single-chip (which is all you need for dual CPU nowadays) Opteron server, though. There are some special lower-power Opterons, but them come at quite a premium, and also take a performance hit.
Even if you want to build your own, server-oriented Socket 939 boards (i.e. with built-in video, optionally built-in SCSI) are few and far between.
If you REALLY want low power, there are a small handfull of boards available that take either Intel or AMD chips that are meant for mobile applications.
If you don't need a speed demon, there are some additional options using alternative chips. (Non-AMD, Non-Intel.) But not dual. Surprisingly, these ARE fairly readily-available in pre-packaged form. Do a search for "short-depth server". There seems to be a niche for these short-depth (typically 14") 1U low-power servers. They can be packed into both the front AND back of a typical enclosed cabinet due to the short depth.