What are the pros & cons to install a 64 bit AntiX system instead of a 32 bit version with 686-pae kernel? What are the differences?
Target system has 8 GB of RAM.

When I ran 64bit AntiX 13.2 on my IBM M57 with just 4 gigs of ram.
It was snappy and trouble free.

The only reason it is not on there now is that I played musical hard drive swaps and went with different hard drives and
just tried something different for the heck of it.

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As far as 1 being more pro than the other. I don't know as I never ran 32bit AntiX on that IBM computer.

About the only difference I remember is that the 64-bit will utilize memory up to 1 Terabyte.

Here's a better explanation from Wikipedia:
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It seems that the 64-bit OS is better suited for scientific and heavy video transcoding (number crunching). Otherwise, a 32-bit OS will run with no problems.

Now I have noticed on my laptop that a 64-bit version of antiX uses LESS memory normally than the 32-bit version. I have been tinkering with 13.2 in 32-bit and amd64 flavors.

A 64-bit CPU will run either version. And some kernels can utilize the 64-bit architecture better than the 32-bit kernel. That's about all I know from present experience.

I don't think a 'normal user' will see any difference other than maybe a little bit more ram usage.

Programs need to be written & compiled especially to use the 64bit registers, as far as I know, most regular programs are not.

It is likely that 'scientific' number crunchers are, so if that is where you are heading use a 64bit distro, otherwise the choice is up to you.