use of a USB HD on 2 different distros

One machine is Slackware 10.2 the other machine is CentOS 4.2

It's an 80 GB USB HD drive ext3

My boot HD's in both of these are scsi, sda. So this USB HD shows in
both computers as sdb5 (its full HD is logical partition ext3)

Works fine on both computers.

But, on CentOS, any Slackware created folders/files show as "user 1000"
and lack write permission for me, user al

And, on Slackware (KDE), any CentOS created folders/files show as "user
500" and lack write permission for me, user al

I admin both of these machines and I'm also the only user on them, user
al ie /home/al

I want user al permissions/access to all folders/files always on this
USB HD no matter which of the 2 computers this HD happens to be on.

But I don't know how to go about that. I guess as root I could issue a
recursive chown. But I suspect it wouldn't last. And I suspect that
there's a better way.

How to? Any help appreciated.

Alan C