Quite a bit of noticeable changes, and from what I've seen, it's between a mix of under-the-hood and graphical.
Nautilus has tweaked a bit and looks a bit different, but mostly with the file save/open dialogue - the open/save buttons that used to be at the bottom of the window are now at the top (possibly to make it a bit more accessible?).
The combined menu (top right one) now has a "Location" entry, which I assume is for any sort of ARM install (phones/tablets/etc) that has a GPS and/or cell connectivity.
Hitting the "Activities" after a cold boot no longer takes the time it used to and appears instantly; however, the trade off is that hitting "Show Applications" now takes a bit of time to load. This is good for those who have things to quickly get to in the favourites bar right after booting, and bad for those trying to use this with a lower-end system (more on this in a bit).
The installation screens to install have also changed (mostly graphical), along with the suggestion partitioning scheme. With 13.1, it used to be that it'd suggest "x" amount of space for swap (since I've almost always had a swap partition, I don't know what the default suggested swap space is), "y" amount of space for "/" formatted as Ext4, and nothing more. Now it suggests "y" amount of space for "/" formatted as BTRFS, and "z" amount of space for "/home" formatted as XFS. While I'm not sure if this change will continue to carry over to the actual 13.2 release, it's a just different from what I expected.
While I'm on the topic of BTRFS, I searched around a bit and found a comparison between it, Ext4, and another commonly used Linux file system (might have been XFS?). From what I remember, BTRFS has the reliability, while Ext4 has the file-access speeds, and this is why I've decided to stop using BTRFS for testing. Though it honestly doesn't matter what file system I use to test with, why not test what I'm going to actually be using? Though I could test twice, but it's a bit out of my league to test the file system, as I haven't a clue how to properly test it - it'll be something I'll have to look up.
Unfortunately for me, I was unable to test VLC like I usually do, seeing that the H264 codec was missing from the repository. I may use a different file format to test, but I'll probably just see what happens in beta 2.
Rhythmbox is updated, and doesn't seem to exhibit the "album art crash". The other crash I can't immediately test for, as it requires me to play hours of music (Rhythmbox crashes after quite a few hours of music, so I'm not sure if it's a specific song/artist/album or just a random occurrence).
While I've technically given up on the Iris icon set, I did test it, as I found it on Triela's drive; however, results weren't any different - it still doesn't work. One thing different is that instead of replacing the window icons (close, settings, etc.) with icons to show you that it's broken, it just uses the default GNOME ones.
That was all the changes I noticed that I could find under my normal "usage". I'll need to do a bit more testing, but I'm thinking I may upgrade to 13.2, seeing I really like not having to wait for the "Activities" screen thing to load.
On the Dell, it operated decently fine; however, "Show Applications" causes 13.2b1 to crash and force a log out. I'm assuming I'm probably going to have to upgrade the processor to a dual-core, since it seems like it's unable to load the applications list correctly. I can, however, search the applications I want to run to start them that way, but that'd be something to get used to.
On Triela: 13.2b1 is fine in itself, and is how I was able to test my "usage". The actual problem I had was with the installation and myself. I was a somewhat tired while installing 13.2b1 to the test partition and didn't thoroughly look over the partitioning summary, which caused it to format my 13.1 partition to XFS to use as "/home". So what was supposed to be a quick 1-2 hour test, turned out to be a 3-4 hour ordeal to reinstall, update, and setup 13.1 close to how I had it. At this time now, I've got it even closer, but I need to use Firefox sync to partially set up Firefox without having to do much. While I'm lucky I didn't lose anything important (if anything at all), it's still annoying. Needless to say, I'll be more careful next time.
I might update if I find anything more after a bit more testing, and if not, I'll be back for 13.2 Beta 2!