Activate network-wide vs site per site & memory allocation

Hi folks,

After struggling with some memory allocation issues (that I have finally worked out *happy dance*), I'm just curious about whether activating a plugin on the network is more resource-heavy than activating it site per site. The given here is that all sites (except maybe the main site) would be using the plugin in my scenario.

Thoughts? Opinion? Experiences to share?
thanks!
-jennyb