any other realtime programmes running at startup? this may not necessary be antispywares/antimalware tools (eg. defragmentation tool?)
try disabling them and see if Avast! uses less cpu cycles.
this is because there maybe odd conflicts between Avast! 7 and the old programme u have while Avast! 6 may not
if the above is true, u may want to do a bug report with ur operating system/screenshots
if the above does not hold, maybe u want to stick to Avast! 6 until the resource usage is improved
on the sidenote, Avast! 7 on my pc uses less than 10% cpu when i am surfing the net but my system startup is a bit slower, about 5s?