re sprockets; shimano 7s sprockets (except in IG which were slightly thicker) are nominally 1.85mm, going to ~1.8mm for 8s and a gnat's less than that for 9s (1.78mm or 1.75mm for campag). Older 5/6s stuff used mostly 2mm sprockets BITD but since the manufacturers use the same sprockets on 7s freewheels as they do 6s ones even 6s ones tend to be 1.85mm these days. (BTW 9s chain is narrower internally though; the same internal width as 10s and 11s; most 7/8s chain will run happily on 2mm thickness chainrings and sprockets in a derailleur system, but 9s chain won't).
So based on thickness alone 7s stuff doesn't have a big edge over 8s or 9s. Death by a thousand cuts applies as you go higher and higher though; some 10s and all 11s are 1.6mm thickness. As important is probably the way sprockets are made; old UG sprockets were noticably harder wearing than any HG, and HG type ones vary depending on who made them. For example sun race sprockets (both freewheel and cassette) seem to be harder and more brittle than many; no good for an MTB with shifts under load (the teeth break off too easily) perhaps but potentially more hard-wearing on a road bike with non-loaded shifting.
It is worth noting that the amount of wear on a sprocket that can stop a new chain from running properly can be tiny; too small to measure even, a tiny change in the shape of the teeth is enough. You can see very bad wear easily enough, but seeing when a sprocket is just
too worn is (IME) impossible. Ten microns in the wrong place seems to be enough difference to make a sprocket work or not. Occasionally I have seen brand new sprockets that cause skipping in new chains, simply because they were not made well enough.
The mechanism of wear seems to be that there is always some wear rather than none, but that the tooth shape is preserved (well enough) provided the chain that is doing the wearing is itself not too worn. The speed of such wear seems to vary enomously with pedalling force; I have seen cassettes that barely look marked and the chains that have run on them are worn to over 1%; this seems to happen with folk that don't push hard on the pedals, or spin nicely; strong folk and 'mashers' can knacker sprockets with a chain that is a little over half as worn as that.
Once the chain gets elongated two things happen;
a) the load is less well shared between teeth, so the load is more concentrated on one tooth at a time (OTAAT..?) and
b) the rollers move more on each tooth whilst under load.
The effect of a) is profound; anyone who has run a chain out to (say) 1.5% will likely have got to the point that the chain runs rough on the least worn sprockets; for example the climbing sprockets if they are not used often, with a "grrrr....grrrr.....grrrr...." sound emanating with each pedal stroke. In a lot of HG sprockets, the tooth loadings can be so high (vs the strength of the steel) that the sprockets actually start to burr over if you use a small chainring and/or pedal forcefully. The most used sprockets can be thus damaged in a little as a single ride. If the sprockets are hard/brittle enough, it is this which breaks teeth off wholesale even if you don't shift gears clumsily.
The effect of b) is more subtle; I think it wears the chain at the interface between the rollers and the outside of the half-bushings, but that this is usually the least significant form of chain wear. However it also wears the sprockets a bit faster than normal, until the tooth shape is once again a good match for the chain. Both sources of wear must generate wear debris, and this ought to be removed from the system since it makes what is often known as 'a third body' in the wear system, i.e. road dirt or not, you make yourself an abrasive sludge, right where it does most damage, inside the chain.
If you ride for a few hundred miles often a new chain will elongate slightly as start to work OK with slightly worn sprockets that didn't want to play ball at first. However this is tedious work, since the most used sprockets are the ones that are most likely to skip in the first place.
I have a strategy for dealing with this situation, a 'cunning plan' if you like. Take a newish chain that is worn to 0.2 or 0.3%, set it aside and replace it with a new one. The slightly worn chain is your 'fallback chain', and you can use it should there be a sprocket that skips when a new chain is fitted later on. After a few hundred miles the bad sprocket should have been worn to match the fallback chain well enough, and the cassette should usually then accept a new chain without further trouble. Use the new chain to 0.2 or 0.3% and set it aside; this is then your new fallback chain. Refit the old fallback chain and change it out as normal, i.e. when it is worn to ~0.5 to 0.75% (depending on how you pedal).
FWIW wipperman published some chain wear test results a few years ago (comparing chain wear rates in different chains) and in many cases they manifested a distinctly 'J' shaped characteristic, i.e the rate of chain wear was low to start with (after intitial settling) and increased somewhat as time went on. IIRC the chains in their tests were not intensively cleaned and there may have been an element of the wear that was corrosion related (if water penetrates the bushings corrosion mechanisms can greately accelerate wear without obvious signs of 'rusting' per se). IIRC the comparison was such that the best chain (theirs, under the conditions of test) lasted at least twice as long as the the worst chain on test. However the thing that caught my eye was (after settling had occured) the low initial rate of chain wear with many chains
. This is presumably some combination of
1) a very thin, hard, layer in the chain bushings
2) a gradual deterioration in the chain lube (which affects corrosion-related wear as much as anything else)
3) the formation of the 'third body' of abrasive sludge (dirt and wear debris).
Now there is nothing that can be done re 1) and indeed it is difficult to know if it even applies. But 2) and 3) are things that are within your compass; by lubing and cleaning the chain, it may be possible to keep the wear rate of the chain nearer the initial (rather than final) wear rate. If you can do this then the projected life of the chain may be much longer than it might be otherwise.
How often should you clean your chain? That is a tough one, but if you flip the question on its head you can get a good answer; 'how long does it take to ruin an un/poorly-lubricated chain?' can be answered. In an LBS near me they use KMC chains in the workshop and the usual life of a 7/8s one is 1000 to 2000 miles (given no cleaning and the occasional splash of oil). The same chain can wear out (to ~1%) in as little as 200 miles if it is not properly lubricated. [This experment was (unwittingly) done by a customer at the LBS; he degreased the new chain and lubed it with some waxy rubbish that didn't penetrate the bushings but just sat on the outside of the chain, a bit like like bird droppings might (in fact bird droppings might have worked better...). A couple of weeks later he returned to the LBS saying 'this chain is no good....'
. They replaced it with another identical chain and suggested that he did something different with it, like not wash all the factory grease out of it; it is (with many chains) the best lube it will ever see.]
The interim 10s wipperman chain test results (included because of clear bmp)
final 10s results (best quality I could find, you can just make out which is which)
11s chain wear test data
In brief the results suggest that there are (very broadly) three categories
1) basic chains; most SRAM, Yaban, cheapest KMC etc
2) midrange chains; most shimano, some wipperman, most KMC
3) most wear-resistant chains; including campag and best wipperman
Some chains wear slowly but are hampered by being not very well made to start with, (eg the KMC X10L silver model). This probably varies from batch to batch, and it may be that some 'selection bias' was applied by wipperman to the chains that were tested..
The conclusion is that, if you change your chain in good time (i.e. before it wears the cassette and chainrings), even cheap chains can offer VFM. In 11s, a sram pc1110 costs £11
and it lasts at least half as long as a £25 chain. One advantage is that you don't have to clean the chain whenever it is replaced.
OTOH if you intend to destroy everything at once (chain, cassette, chainrings) there is something to be said for buying an expensive chain.
The chains that might have the best 'TLC to increased life' ratio might be KMC 'XX' treated models eg X10L, X10SL, gold, silver variants.
if you can buy them cheap (e.g. reduced to ~£20 at some retailers presently) the midrange connex chains such as 10-SO models are good value too.