It seems that one of the main advantage of CPUs that are marketed for servers (e.g. the AMD Opteron and Intel Xeon) over CPUs marketed for consumers (e.g. AMD Phenom II and Intel i7) is related to reliability under thermal strain.
The response given on superuser.com to the question "Advantages of server-versions (Xeon, Opteron) of CPU's" totes a common line in my searches on Google for an answer. The claims typically involve three categories of advantage (which are quite regularly repeated):
1. Heat resistance
"Server" CPUs are better able to withstand more heat for longer than their "consumer" counterparts.
Presumably the advantage would be that the "server" CPU would last significantly longer before dying if the fan cut out, or alternatively requires less cooling.
2. Performance and optimization
"Server" CPUs have faster speeds or are optimized for server tasks, for example from the link from techpowerup.com stating the advantages of a "server" version:
Tweaked memory controllers, Cache sizes, thermal outputs, voltages, testing scemes, HT links, pricing, included heatsink, speed binning, many things.
First of all opty's are tweaked for higher throughput vs latency. Also their cache sizes in reguard to their speed is also larger. Voltages and TDP are lower compared to their equivelint x2 or phenom units.
"Server" CPUs have certain features the "consumer" CPUs do not have, e.g. "HyperThreading and Virtualization Technologies" (from the Superuser link), or support for error correcting code (ECC) memory.
Of the above advantages commonly toted as the basis for CPU manufacturers selling their "server" versions at significantly higher prices than the "consumer" versions, I'm particularly skeptical of the claim of thermal resilience. So let's ignore claims #2 (performance) and #3 (features).
I'm skeptical of greater reliability in general, but I think it's fair to say that a significant portion of CPU failure is, in regular consumer and server usage, related to thermal resistance (i.e. heat increases the rate of failure).
Rather than differentiation between reliability based on "server" or "consumer" branding, I'd expect that all CPUs of a similar die size would have similar thermal resistance qualities. In other words, I think die size plays a much larger role than branding.
Are server CPUs more resilient to the effects of heat than consumer CPUs of the same die size?
EDIT: Edited the above to limit the claims to thermal strain (i.e. removed "features" and "speed"), as per the comments of Fabian and others.