It really depends on what the server is supposed to do.
There are servers that continually handle thread after thread after thread with very little need for actual single-threaded efficiency. OLTP servers are mostly like this. Here, the more cores, the better - for example, Apache/Mongrel/Tomcat + PHP/Python/Perl/Ruby/Java, and using a database almost purely as a datastore. Some implementations of Lotus Notes can be seen that way as well, especially if a lot of the processing is done client-side.
Then there are servers that not only serve multiple users/clients, but also need to process tons of data to generate complex reports. Here, single-threaded performance is as critical as having as many cores as possible, because each request can require a good chunk of processing power. Any web-based, or client-server type system qualifies as long as it contains a big database and produces meaningful reports of any sort. LAMP stack systems and Lotus Notes implementation with no LN clients installed (clients connect through the browser), for example, can easily demand high single-threaded performance, especially when deployed in large enterprises. You just don't want to see an Atom-level server (even 512 Atoms in a box like SeaMicro) execute a multi-join query on tables with millions of rows, loop through the results, and make one or a few more queries for each result retrieved from the original multi-join query, plus a few more math operations on the data.
Sometimes, a server may only need "occasional" single-threaded throughput. For example, most of the time it acts as a simple OLTP, but then every morning it is expected to perform a batch job that requires much computational power, and it has to end before the daily transactions start. In such a case, SeaMicro type solutions may not be feasible if you want to just have one server for the job, and the batch job cannot be parallelized. Similarly, we can also concoct a use-case where SeaMicro types would be perfect or perfectly acceptable. It just depends on the requirements, and just how critical or time-constrained the batch job is.
EDIT:
As for "performance per watt" - this is sometimes misleading. If the server demands high single-threaded performance as in examples above, then a CPU with better performance per watt on paper may not give better power savings in the real world, especially if the advantage on paper comes at the cost of performance. Johan covered this in his latest article. The faster processor can finish a job faster and then return to low-power/power-saving mode faster than the "energy efficient"/"low-power" processor. When this scenario happens often, there is little to no power savings gained from going "low-power"/"energy-efficient", and you have inconvenienced the clients/users by making them wait longer for their report to finish.