Your question isn't very clear.
By itself Apache wouldn't affect one site differently than another all things being the same.
A poorly written script or a page that uses a very CPU intensive process can result in high CPU use (for example a forum that has a bunch of poorly coded "add-on" scripts installed-removing one "bad" script could make a huge difference)
However we don't know if you are speaking as a server owner having problems with a web site or as a web site owner having problems with your host/provider telling you that you are using too much CPU for their TOS.
If it is the latter it can surely be affected by what their CPU is capable of and the memory etc. as others have mentioned.
For example (to clarify some of the above answers)
If you are a web site owner and your host is saying you are using too much CPU:
If the terms of service are based on a % of CPU which you are allowed within "X" amount of time:
2 servers are both running Apache and server "A" has an older "plain" hard drive, an older Celeron processor and 1GB memory :sad:
Server "B" has a new fast quad-core Xeon CPU with 8GB of memory running SCSI mirrored disks or SAS disks
You would use a greater % on server "A" than server "B" just because of the difference in the server.
It would be because of the amount of resources available not because of Apache.
We could be more helpful if we knew more about the situation you are in.