I bought Samsung Galaxy S2 & Samsung Galaxy Note 10.1 couple of years ago and for the better part of the last half a year both devices became unbearably slow. I went through the usual motions of cleaning junk and cache and memory but nothing helped, so I just kinda written of bad performance as a case of “applications becoming more bloated and device performance staying the same”. However, recently I read that Android didn’t have TRIM support until 4.3 version (more about this here). Problem is, that highest supported version of Android by Galaxy S2 and Galaxy Note 10.1 is 4.1.2. I didn’t want to try custom roms, so I tried fixing my performance using third party software Trimmer (fstrim). Before trying this program you need to have your device rooted, you can read about it here (Galaxy S2) and here (Galaxy Note 10.1).
Running Trimmer (fstrim) software alleviated performance problems significantly.
P. S. There is a chance to brick your device by either rooting or running trimming software, so do it at your own risk.