Is it good to keep apps closed on iOS devices? Is it better to keep apps closed (double tap home button, hold the icon, and exit the app), as much as possible on iOS devices? I know the more apps one has open, the more RAM, for example is used, but would that same principle apply, in measurable effect, to iOS? 

For example, would my iPhone (4S in this case), or iPad (3rd Gen) run any faster, or have longer battery life, or do better in any particular way if I had only 5 apps open, versus having 50 open?

Side note: I know there are some apps that don't handle multi-tasking very well (possibly due to a lack of programming expertise?) and hence will deplete battery life while running in the background. I'm not necessarily talking about those.
iOS at its core now has its own multitasking API built in. The only way for an app to even go into the background it has to use these API's, so even poor programming experience still can't ruin things too much (and, with the flip side of that, poor developer experience could make the app while its running use more resources than needed). 

All in all - this shouldn't be an issue. Those apps in the tray don't mean they are running - it literally is also a recently used app tray. And again, the background tasks they can do are limited by the backgrounding API, so like audio, VOIP, navigation, uploads, etc. 

As far as being faster, have longer battery life, etc - no. At least not on an average. You may feel that it runs different, and yes there may be a rouge app doing something odd,  and forcing it closed may help. 

But in general, no - this shouldn't affect speed or battery life, unless those apps are currently doing background tasks such as location, audio, uploading files, etc. Otherwise, their RAM state is saved for quicker relaunch, but no processing power is being used.