Local vs. remote Piwik installation?

I’ve been thinking about consolidating multiple Piwik installations into a single server. I wonder about experiance anyone would have about such move. How much difference there is for sites that have up to 3,000 visitors per day?

Local Piwik installation is certainly faster than remote one - that’s for sure. Still, for easier management, what do we gain or lose if/when we consolidate multiple installations into a single server?