If you don't need the dynamic and wide range of features of Apache, thttpd will probably give you a better performance.
thttpd's model excells as the network transfer overhead outweights processing time (which is the case for static files, espicially large ones).
In Apache, a process (or thread) is started for each request to do the initial work of opening the file, executing the script, .. etc. But then it spends the rest of its time doing nothing but sending the contents over the network to the client.
Some of the busiest sites in the world are still running apache. You might just do some tuning of your apache server and it's configuration file (whether you upgrade or not).
Of course the super busy sites have multiple servers and reverse proxies.
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