This post is my thoughts on this well intended, but slightly misguided, post on Digital Photography School.  NOTE – this post was written in June of 2016, if something changes, updates will be noted here.
Personally, I always shoot at 14-bit Compressed RAW.  For me, it is better to shoot at 14 vs 12.  While using 14-bit does create larger files, for me, this is not an issue.  But, I do not work weddings or sports where shooting 14-bit may clog down the system due to processing large numbers of large files.
Now, I like math.  I like math a lot.  I also understand light and electronics.  Here are my thoughts.
14 bit raw does not buy you much except when it does.  To fully explain what it buys, I have to explain how your eye works vs how an image sensor works.  I’m going to use an example.
If you take a room with 1 lit candle, then add 1 more lit candle, your eye will really notice the difference.  If you take a room with 1000 lit candles, then light one more, your eye will not notice this at all.  This is because your eye works on relative brightness.  Doubling the light is very different vs an increase of 0.1%.  However, a camera works off of absolute brightness, which means that both examples are the same increase in brightness, or an increase of 1 candle.  Minute Physics has an explanation of this.
With the Gamma Curve, and relative brightness levels, what does the bit-ness mean and what does it give you?
The simplest answer – the bit-ness matters in the shadows and the shadow detail.  If you have a well lit scene with very little shadow detail, there will likely be no easily discernible difference in 12 vs 14 bit.  There will certainly be differences between 12 and 14 bit RAWs, but they are mostly in the file size and the after capture flexibility.  The less you want to push the shadows in the final image (vs at capture) the less 14 bit matters.  If you shoot HDR or shoot brackets for some kind of HDR usage, you should be fine with 12 bit.
In this part, I do not disagree with the DPS post.
Where I do severely disagree with the post is in compression.  This part of the discussion shows where the author lacks computer science skills.
Side note – this is about lossless compression only, and is based on my experience with Nikon cameras.  This does not cover lossy RAW, which is available on Nikon and Sony cameras.  Nor does it talk about sRAW files.
Much like how in photography every choice you make is a trade-off, compression is the same.  But in compression, the trade-off is more interesting.
Let’s take a file that is 100MB.  In this situation, the file can be compressed to 60MB with 1 additional second for processing time.  This file can be uncompressed with a modern CPU in half a second.  The question very quickly becomes — does compression make sense?  The next question is, how long does it take to compress the file, and is the storage system able to handle uncompressed vs compressed faster.  For storing the file, if you can transfer 20MB/sec, the 100MB file takes 5 seconds to transfer and the compressed file takes 1 second to compress and 3 seconds to transfer, for a savings of 1 second.  If you can transfer 100MB/sec, the larger file transfers in 1 second, and the smaller file transfers in 1.6 seconds.
If you shoot compressed RAW, opening the file on a computer later could take slightly longer (due to needing to decompress the file).  But a computer normally is fast enough that this doesn’t matter.  You may not notice a difference in the compressed file vs the uncompressed, especially if you have a SSD and a CPU from the last 3-4 years.
Compression may shorten the battery life on your camera.  The longer the camera CPU and sensor are idle, the better your battery life.  Transferring and compressing both use power.  With a relatively new camera, this is unlikely to make a difference of more than 5% change in the number of images per charge.  My DSLRs can shoot nearly 1000 images on a single charge, so +/-50 isn’t a huge deal.  With a modern camera and a slower memory card, it is more likely that you notice that images save faster if you use compression.  Only once you hit the fastest of the fast for memory cards (say, a latest generation QXD card) would compression increase the time required to save a RAW to the memory card.  I am not saying you should buy cheaper cards, but I am saying that most people will not need the fastest generation of cards, and would be better off buying 2-3 of the previous generation of cards for the same price.  Also, if you compress your files, they will take up around 30% less space on the card, making those 3 64GB last gen cards even better than the 1 128GB current gen card.
In short, the math proves that for the vast majority of people, compressed RAWs will be a benefit.  I will be happy to edit/append this post if I am wrong within the next 2-3 years (note, the year this post was written or updated).
-Brad