64MB video memory is plenty for running even the newest version of Ubuntu with all desktop effects. What's more, 2GB is plenty of main RAM to run a full Gnome/Compiz/Unity graphical desktop.
If you are experiencing slow performance it's probably not so much the amount of video memory but the overall performance of the system. A Pentium 4 is pretty old, your onboard graphics is also probably quite slow, and you may also have a slow hard drive if it's from a similar era.
Alternatively, it could be that your system is not running in accelerated graphics mode because of a problem with your system, which in 12.10 would mean that you're running software-emulated (which would be slow).
12.04 and 12.10 are not different enough architecturally that you should notice any significant difference in performance from them on the same hardware. One notable difference however is that 12.04 has an optional "Ubuntu 2D" mode whereas 12.10 doesn't. Ubuntu 2D may work better on systems without 3D acceleration (or with buggy/poorly supported 3D acceleration) than 12.10.
Things you could try:
Switching from Gnome to XFCE.
This can be done by installing Xubuntu, a version of Ubuntu which pre-selects XFCE for you, or by switching desktop environments on an already installed Ubuntu.
XFCE is a lot more light weight than Gnome, but most of this light weight is in the form of memory and resource usage (and with your 2GB of RAM, that's probably the area where you have the least problems). So you may or may not notice a huge difference.
Run Ubuntu 12.04 in Ubuntu 2D mode.
Ubuntu 2D mode has been removed from subsequent versions of Ubuntu. It is an alternative mode which doesn't make any significant use of graphics hardware, yet still has pretty much the same usability and compatibility with Ubuntu Unity. If it's a graphics card problem, this will at least work.