I wouldn't expect it to be any faster, especially if you are comparing the performance increases of doing the same thing on an Android device.
The reason is that, on an iPad, Apple goes through a great deal of trouble to ensure that applications don't mess up your operating system (e.g. by using up too much resources in the background). Compare that with a Windows or Mac system where each application you install can load up its own background processes. In an environment such as that, you would expect a reset of the entire computer to speed everything up.
The only thing affecting your performance on the iPad, however, is iOS, which Apple provides. Assuming you reset to the same iOS you are currently using, you should expect the experience to be the same at the end.
My guess as to why your iPad is less responsive than it used to be is that Apple is optimizing their iOS updates for the newer generation iPad models rather than worrying about how it might affect the user experience on the 1st generation iPad.
Therefore, I think the only thing that could potentially increase your performance is if you downgrade the iOS on your device (which is beyond the scope of this answer), or wait for Apple to release an update which fixes the issues you are experiencing (unlikely with older generation iPads). A final option might be to jailbreak and see if there are any solutions available there (I'm not familiar with jailbreaking, so I can't point to specifics).
The one caveat might be that you are running multiple applications (several of which may be consuming up resources). However, the fix for that is to simply shut them down rather than reseting the entire iOS.
I don't believe there are any software differences at all between an iPad mini and an iPad 2 or iPad Air. Both iPad minis use the exact same display resolution as their larger counterparts (1024x768 non-retina, 2048x1536 retina), just on a physically smaller screen. The whole purpose of this is to ensure that all existing software works identically on both device sizes.
In fact, I don't think it's even possible for an app to "know" which size device it's running on, since there's no technical way to differentiate them. Apple's own iOS Simulator doesn't even list the iPad mini as a separate device to simulate: the only options are iPad (meaning 1024x768) and iPad Retina (meaning 2048x1536).
Best Answer
Apple maintained support for all iOS 8 devices in iOS 9 but that meant that some devices couldn't fully support some of the new features. If it's the first generation iPad mini you have, drawing in Notes is not supported. Support starts with the iPad mini 2.
I haven't seen anything about Siri Suggestions not being supported. You could verify that your device is supported and Siri Suggestions are turned on under Settings > General > Spotlight Search. There should be a toggle for Siri Suggestions if supported.