S&F vs machine kneading

Both are sound techniques if executed properly.  In fact stretch and folds are often used after machine mixing allowing for the initial mix to be kept shorter and build the gluten during the bulk fermentation phase via well timed stretch and folds.  Some say they should be in the early stage of fermentation while others like to have them evenly distributed throughout the entire time.  Check out the slap and fold technique another great way to hand mix dough.  

Josh

I always knead my dough to a certain extent more so with high protein flour, then do some stretch and folds. If I am going to bake the same day I space out the folds every 45 min or so. If I am going to put in the fridge (retard) for further slow flavor development I time the folds less say every15 - 20 min and put in fridge to develop more slowly.

If you autolyse the water/flour which is a very good idea, this essentially does half the kneading for you and you will realize how elastic your dough gets during kneading much quicker

Josh has pretty much summed it up

Just to expand upon what Josh said already, yes, they are just different methods for developing gluten, and each good in its own right.

Some people prefer different techniques for different breads - for example, making Tartine-style sourdough boules using an autolyse and gradual stretch and folds to develop the gluten while preserving the air bubbles, but then using a mixer on high speed to make a lightly enriched pain de mie style pan bread.

I like hand kneading my bagel dough because it's dry enough that I don't need any flour on the counter, so I don't worry about throwing the hydration off while developing it - and also I killed a mixer once making it. Whereas with wetter doughs, I prefer using a method that doesn't get the dough onto a counter, where I might need to add flour to keep it from sticking, so that I don't lower the hydration.

So, basically, it's a matter of context. There's a lot of ways to get your dough to the point you need.

I recommend just trying different things and seeing what you like. And do take that suggestion of looking up the slap and fold technique. Dabrownman has a system for using that one with a series of short rests to develop his doughs which you may find interesting. I think this video is a pretty good description of the process, to start you off.

Here's a link to a YouTube video showing the Stretch & Fold technique I used on the 65% hydration bread dough:
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Stretch And Fold A Gentle Way To Develop Dough 

http://www.sourdoughhome.com/index.php?content=stretchandfold
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Panama bread's first stretch and fold
https://www.youtube.com/watch?v=hxqmWxWBDSQ
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Panama Bread's Second Stretch and Fold
https://www.youtube.com/watch?v=kLuMfEJnNW0
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Panama Bread Third Stretch and Fold
https://www.youtube.com/watch?v=Sy52miUA6XE

I like both the no knead or the french kneading method, I do not use the Stand Mixer much.

When I do french kneading I need for about 3 minutes, than I let the dough rest for 5 Minutes, I carry on like that until the dough is soft , smooth and elastic. 

I would suggest to do knead by hand until you get a feel for what the dough should feel and look like at different stages during kneading, it did help me a lot to * get to know the dough * before I ventured in to the Stand Mixer kneading or no kneading.

It is great to get good information and read books BUT , as you noticed yourself, they all tell us different things , which all work well , but also confuses us.

I stick to just a few things now that I know work for me.

You are correct in saying that these techniques are for developing gluten.  Everything we do in the baking world is for that sole purpose! When you knead by machine you use a dough hook and let it work the dough around in the bowl for a while.  Kneading by hand is personally my favorite because you can feel the dough coming to life under your fingers! But you need to be careful not to add too much, if any, flour to your surface or you will throw off the hydration level.  Kneading is best for the stiff to soft and kind of tacky doughs.  Once it gets too wet it's very hard to knead!

The stretch and fold is literally what it sounds like.  You stretch out the dough and fold it over on itself.  This is a slower process then traditional kneading but produces great results. Generally you see the stretch and fold method in higher hydration doughs because they are just too wet to knead!  Plus all of that water is also helping to develop the gluten like you see in the autolyse method.

Both are great and effective methods for gluten development and deciding which is better is completely a matter of preference! 

Here is a great video for some delicious bread using what I like to call the slap and fold (I'm not sure the real name of the technique)!  It's like a cross between kneading and stretch and fold.  https://www.youtube.com/watch?v=kXV8mayG3W0

I like having different techniques at my disposal. For my whole grain/multigrain breads I normally use Peter Reinhart's pre-dough method (from "Whole Grain Breads"). If I don't have time for pre-doughs, or prepare breads without a starter or soaker I often work with brief kneading plus S & F.

Very high hydrated breads like Forkish's or Tartine's I stretch and fold only.

I don't care for hand kneading and like keeping machine kneading as short as possible, so both methods work very well for me.

Karin

learned over the years and each has is perfect place.  I do the old fashioned kneading for very low hydration dough like bagels.  Can't mix with a KA , slap and fold or stretch and fold that dough.  For enriched dough like panettone or very different wet ones like Michael Wilson's 100% whole spelt at 100% hydration, then the KA mixer is King if you don't want to slap and fold for 40 minutes getting dough on the ceiling and everywhere else:-).

But for most of my bread baking between 72% and 90% hydration now a days, it is 3 sets of slap and folds on 10-20 minute intervals with the first one ending when the dough stops sticking to the counter followed by a one minute set and then one of about 10 slap and folds.  I want to get the gluten developed early in less than an hour.  If the dough   is between 68% and  72% hydration you might get by with 2 harder slaps and one fold but probably should just use stretch and folds and skip the slapping.

The slapping and folding are usually followed 3 sets of stretch and folds on the same intervals.  The stretch and folds are 4 each set, from the compass points only,and usually just to fold in the nuts, seeds, fruits, or other add ins plus sort of keep the gluten development in shape as it ferments on the counter. 

Happy kneading