Do unused Cisco IOS features take up RAM/CPU resources? For example, let's compare IP Base vs. Advanced Enterprise Services. Let's say you have advent installed, but you're only actually using the features relevant to ipbase. Other than flash memory space, would running advent when you only need ipbase decrease the router's performance in any way? Or to put it another way, would the router's performance be enhanced (however slight) by running only the IOS feature set that you need instead of the full advent image?

Strictly speaking, yes, the unused features do cost you some performance. However, "measurable" loss is questionable. Most features are initialized even if they aren't used, so that will eat into memory, and any periodic "house keeping" tasks will still get CPU time. The major features (ipv6, telephony service, routing protocols, ids/ips, etc.) have to be explicitly enabled and configured; and yes, they're very much measurable.

Is advent 10% slower than ipbase at doing "ipbase"... No. It'll take a lot longer to boot, but day-to-day operations will see very little difference. (assuming you have the memory to run advent in the first place)