Hello. Sorry for the delay.
Tab 3 or Tab 4? Not sure what model Note 10.1 you have.
So my Note 3 has this when I hold the Home button. It sounds like this is what you are descibing is missing on the Tab 3, but on your Note 10.1.
That's possibly correct for the Tab 3, but I would be surprised. On a more stripped/vanilla Android device you can swipe all the open app thumbnails to either side to clear.
If they are Tab 4's with the newer Touchwiz you have a dedicated button which doubles as a menu button when held.
So I am not a real help, but just to say it's unlikely clearing ram and apps will speed it up and there is probably another reason. Given, it will have a lower powered cpu but still.
Check the Google account settings and uncheck anything you don't need. Take a look at the Battery(x3l and Data usage graphs, and try the GSam app to help isolate what is slowing it down.
Come back if you need more help.
You may get someone more knowledgeable

.