Should I create multiple sidebars, or use or one dynamic sidebar with logic to determine it’s abilities?

Create separate sidebars for each page unless all of them are supposed to display the same set of widgets.

I guess you will be managing your sidebar widgets through Appearance Widgets Screen (which displays all registered widgets) so just use register_sidebar() three times or preferably register_sidebars() (set number to 3) within your functions.php file and then you’re ready to put these in your template files:

<?php dynamic_sidebar( 'id-of-your-first-sidebar' ); ?>
<?php dynamic_sidebar( 'id-of-your-second-sidebar' ); ?>
<?php dynamic_sidebar( 'id-of-your-third-sidebar' ); ?>

Hope it helps. I might be wrong but I don’t really see a point in creating one sidebar and using logical operators to modify them.