I see that there are three kinds of chain wear gauge: The basic kind. I'm used to using this kind:
The hook style. Supposedly provides an indication of how worn the chain is. I've used these and the idea makes sense:
Digital. This seems like overkill and designed to separate fools from their money:
Does anyone know the relative benefits of each? Is the simple kind generally good enough?
"Useful" is hard to define for everyone. For me, "useful" tends to mean "has a lot of uses". The very specific chain wear-checking tools you list above are "handy" in that they do one thing and they do it reasonably well. Useful? Well...if you need to do it a lot and/or it is difficult.
But there is a tried-and-true method using a simple tool that many people already own, and which has a lot of other uses: a tape measure or ruler with inch markings. You simply align an inch mark on one side of a rivet, then look at the corresponding rivet 12 full links away. On an unworn chain, the rivet will line up exactly at 12 inches. A worn chain will be more than 12 inches. On most bicycles, you won't even need to remove the chain to do this. And it works with virtually all modern bicycle chains.
Chain wear in general is a bit of a "religious" issue, but a rule of thumb if you must have one is: within 1/16 of an inch, no problem. Between 1/16 - 1/8 of an inch, probably time to replace the chain. Past 1/8 of an inch, you've probably noticed other issues in the drivetrain.
This (along with many, many other chain-related issues) is summed up nicely at Sheldon Brown's site (see 'Measuring Chain Wear', towards the bottom).
The first one -- the simple Park Tool gauge, is perfectly adequate for most uses. It provides two levels of indication, and is reasonably inexpensive and foolproof. The second one is maybe a little better, in that it gives you a sense of how close to the "break points" you are.
With either of the first two, and some other designs, one needs to be careful to not "force" the gauge -- too much force not only yields bad readings but also will damage the gauge.
With most gauges the chain needs to be measured while under tension. For a standard derailleur setup simply measuring the top chain segment while on the bike generally suffices, but for a fixie you will need to apply modest pressure to the pedal to make the chain taut (unless the tugs are tightened all the way to begin with), and if the chain is not mounted you will need to manually stretch it or apply a weight. The force does not need to be a lot -- just enough to press lubricant out from between pieces, etc.
The referenced article enormously overstates the potential error from roller wear. If you're measuring over 14 links like the Park tool, you accumulate 14 links' worth of "stretch" but only one link's worth of roller wear, so roller wear is a negligible contributor to the measurement.
The best ones by far: Shimano TL-CN40, TL-CN41 or TL-CN42. Unique amongst chain tools in that they are as accurate as the ruler method, with the ease and quickness of the slot in tools.
They are the only "tool" to do this, i.e. they measure pin wear only, roller wear (which does not matter) is eliminated. Not cheap though, but they are the best and certainly will be worth it in money saved.
I have been recently looking into the question of measuring chain wear, and in particular, using a 12" steel rule, or ruler. The 12" ruler I have has markings at one tenth of an inch, so I found it easier to measure a 10 inch section of the chain, then the critical 1% wear equates to one tenth of an inch, (which is 1% of ten inches). When measuring the chain, if the rivets line up at 10", the chain is like new, but if the rivets line up at ten inches, plus one tenth of an inch, the chain is 1% stretched, and anything between 0% and 1% stretch can be visibly judged for a 0.5%, or a 0.75% reading.
The first one you posted is good because it's cheap. However, it lacks the ability to measure a chain until it's worn out, or really worn out.
The second one is still cheap and gives you the ability to measure your chain at an earlier stage of wear. Downside is you lose some compactness. I have not used that type before so i cant speak to its accuracy.
The third is really for shop use and may be overkill even in that situation. Digital calipers are really nice to have, but you don't really need that same degree of accuracy in a chain checker, so in my opinion this is a little wasteful of your disposable income.
A couple other options that you didn't post are the Park Tool CC-1 (which is no longer made) and the Park Tool CC-2. As you might expect, the CC-2 replaced the CC-1. The CC-2 is a little more expensive than the first two checkers you posted, but definitely far less than the third. It has a compact design so it's easy to throw in an already cramped toolbox (like mine), it's very easy to use, it gives an accurate reading, and it should last a lifetime for personal use. It's the one you're most likely to see shop mechanics using, yet it's still very affordable.
I reference to djangodudes answer the 12 inch rule works fine, but I would avoid a tape measure,use an inexpensive steel ruler.If you must use a tape, measure from the 12 inch mark to the 24 inch mark.Doing this eliminates using the hook at the end of the tape which can have movement that will skew your measurement
I use the Park Tool CC-3, but as jm2 mentions it's only a "go/no-go" indicator.
I tend to remove my chain periodically for cleaning (due to lots of mountain biking in wet/sloppy conditions). To get a more nuanced view of chain wear, I took an old chain (one that failed the CC-3 test) and nailed it to a wall in my garage. Now when I remove my current chain to clean it, I hang it next to the old "known bad" chain and eyeball the length difference.
This is only practical if you have an easily removed chain, such as the SRAM "powerlink" models.
