the specs for cs3 are fairly high IIRC
from the adobe site
Windows
* Intel® Pentium® 4, Intel Centrino®, Intel Xeon®, or Intel Core™ Duo (or compatible) processor
* Microsoft® Windows® XP with Service Pack 2 or Windows Vista™ Home Premium, Business, Ultimate, or Enterprise (certified for 32-bit editions)
* 1GB of RAM for DV; 2GB of RAM for HDV and HD
* 3GB of available hard-disk space plus 2GB of space for optional content (additional free space required during installation)
* 1024x768 monitor resolution with 32-bit video card; Adobe recommended graphics card for GPU-accelerated playback
* For OpenGL support: Adobe After Effects supported OpenGL 2.0 card (NVIDIA recommended)
* DVD-ROM drive
* QuickTime 7.1.5 software required to use QuickTime features
* Internet or phone connection required for product activation
* Broadband Internet connection required for Adobe® Stock Photos* and other services
* For recommended graphics cards and compatibility lists, see the OpenGL page.
Macintosh
* PowerPC® G4 or G5 or multicore Intel processor
* Mac OS X v.10.4.9
* 1GB of RAM for DV; 2GB of RAM for HDV and HD
* 3GB of available hard-disk space plus 2GB of space for optional content (additional free space required during installation)
* 1024x768 monitor resolution with 32-bit video card; Adobe recommended graphics card for GPU-accelerated playback
* For OpenGL support: Adobe After Effects supported OpenGL 2.0 card (NVIDIA recommended)
* DVD-ROM drive
* QuickTime 7.1.5 software required to use QuickTime features
* Internet or phone connection required for product activation
* Broadband Internet connection required for Adobe Stock Photos* and other services
* For recommended graphics cards and compatibility lists, see the OpenGL page.
*Online services, including, but not limited to, Adobe Stock Photos and Acrobat® Connect™, may not be available in all countries, languages, and currencies. Availability of services is subject to change. Use of online services is governed by terms and conditions of a separate agreement and may be subject to additional fees.
if you dual-booted xp (maybe vista?) on the mac you should be able to use AE (if you only have the pc version). I think you have to have the macs with the intel chip in it, but I'm not so sure about that one.
as far as I know there isn't a "patch" to let you use one version on the other system