Is there a speed penalty for making a simple plugin vs. a theme function in WordPress?

Architecturally, there should be no difference. Wordpress themes and plugins are both simply PHP files. In both cases they are executed via a variation of an include or require call when PHP processes the page. Based on that, I don't believe there would be any difference. I would strongly advocate plugins over themes as theme upgrades will break your feature. It also makes testing much easier as your simple task grows in the future. It is unfortunate that themes are not simply a presentation layer as the name implies. Think of them as a fully custom web application without a common control panel interface. I have some themes (Privateer would be one of those) that are more complex to configure than most plugins. This is commonly overlooked from the site security perspective.

I think the best answer is maybe. While minor there has to be some overhead in WPdeciding if and when a plugin should be well, um, plugged in. Then there's the issue of the plugin itself. For example, maybe it has its own bit of CSS that might have to get jammed into a page somewhere (as opposed to being in the main stylesheet.). That bit of CSS is less than ideal. Again, minor but none the less it's not zero. Then if for some reason that plugin is reaching further back into some API then that too can cause a delay. Mind you, that might not follow under "simple" but then again, maybe it does. Yes, such API usage would show up if it were in the theme, but as mentioned, this on top of the plugin processing delay could add up a bit and effect rendering. Probably not, but maybe - at least a tiny bit. I would say that for simple stuff using functions might be a good compromise. You'll have the flexibility to move functions from one theme/site to the next. But you're not always hardcoding right into the theme - except for the line of code that calls the function. Or something like that :)