Anti squat and anti rise VS shock and fork tune

In my opinion shock tunes can’t fix bad kinematics.  But a bad shock tune can ruin good kinematics. 
 

I need to start with a good frame that has good kinematics, then chassis flex, then suspension tune, then parts like bars and wheels.

Bikes with high AS do not provide good traction on techy climbs ... The best you can do is a position-sensitive damping + lockout and no one currently does that, but it's theoretically possible. But good sensitivity will mean some loss of efficiency anyway, just the bike will not bob like hell. The problem is that AS means you provide a force to keep the bike high in travel vs damping can only slow down the bobbing, so to be effective you need very high damping coefficient which needs to play nicely with bobbing/pedaling frequency, which is very low for a suspension movement perspective.

I think your a lot better off (to your point) chasing frames with good pedaling efficiency throughout travel rather then trying to keep AS and therefore frame squat forced high. Sensitivity makes traction. 

 Also to your point position sensitive damping is horrible in my experience. Speed sensitive seems to work better and you don't want to pigeon hole yourself into using it to mask another problem. To the original posters question, you don't ever want to low speed damp yourself so far to stop bob that it kills your terrain modulation control. A little bob doesn't hurt you with the right frame. 

Fork tune wise, I think supportive yet supple off top is the game coupled with smooth bottom out control. To have all this at once  lack of friction is the most important bit to have it all. Too many forks have bad bushing tolerance or sticky air springs that make both at once impossible. 

There is nothing like "supportive yet supple off top" damping without position sensitive, since classical damping has no "off top" notion at all, it is speed sensitive, that's why tuning it is always a compromise. I think that either you have support from you spring or you will never have supple yet supportive, cause upping your compression means losing suppleness and there are really no ways around it. You always go through the low speed and turning the high speed means that you will lose suppleness on high-frequency chatter. Not to mention that most of the time there is no such thing as HS(C/R) setting, the dials simply "turn on" the HS shimstack at higher speed effectively rising the perceived level of LS, the very force of HS stack is not controlled by the dials at all! (except the VVC and alike).

Suspension in the 2000s used to be highly based around threshold damping as Anti-Squat (AS) was not even a thing back then. The threshold damping did a good job of controlling "bobbing" but was pretty awful for compliance.

Many shocks today still use threshold damping in the from of lockouts, and sneakily in preloaded rebound shim stacks (very common today. Hi Rock Shox) 

The key to all of this is that the threshold to improve pedaling in a shock through damping is a similar threshold that affects the quality initial stroke of the bike's travel. And it's on all the time. 

While AS only affects the shock stroke when pedaling and is off during other times (oversimplified).

Your original question is sort of like when I ask the dentist "What's more important, brushing or flossing?" Dentists hate that question because both actions work together as a system. What's funny is I typically get different answers. They really hate the question and some dentists refuse to answer it entirely, but when pressed some dentists will tell me flossing is more important and others tell me brushing. Obviously, neither is sufficient on its own. Same with suspension. All the elements do different things and all the elements work together to create the end result. And you didn't even mention leverage rate, which for my money is the single most important kinematic parameter. If pressed, I guess I'd rather have a great kinematic and a bad shock, but how bad? If the rebound speed is "molasses," that isn't helpful either.

In short, no - shock & fork tuning can't make up for kinematics, not even close. They are all doing very different things but the shock tune does highly depend on the frame kinematic so if those don't work well you will be very limited in how much performance you can achieve. 

Things like anti-squat are a measure of the vehicles response to acceleration - so an "ideal" AS would mean the bike doesn't move under acceleration so you wouldn't need to do anything else to combat it. If you were trying to add damping instead it would compromise other aspects of performance so you're now chasing your tail with your set up as one thing impacts the next. If you start with a good platform then each part has more room to do its job with less compromise.

It's a bit like the more spring vs more damping question people often bring up - they are different things doing different jobs that are supposed to work together, not one instead of the other

Dude read Race Tech’s Motorcycle Suspension Bible, then report back. Topics covered include chassis dynamics/kinematics  and of course damping. 

(YETI) owners hate that question on the trail. They just want to ride.

Suspensionlabnz thats my take too on this theory. Molasses damping goodness for fresh sand mx tracks equals heaven.

This is a very strange question actually. Anti-rise and anti-squat are properties of kinematics that describe how much movement the rear suspension produces as a reaction to input loads. Basically through geometry of suspension parts the input loads are balanced in a way that the suspension movement is reduced. Typically there are compromises to be made. In regards to anti-rise, zero movement is typically not desirable because of weight transfer to the front of the bike, so there is a sweet spot somewhere depending on your priorities (grip or preservation of geometry). In regards to anti-squat, it's probably pedal-kickback that needs to be reduced, so as far as I know the manufacturers try not go too high on that to make suspension more active while climbing at the cost of having to use the climb switch (which I am not a fan of personally, I don't do technical climbs on my enduro bike and I don't like using a climb switch).

With suspension tunes it's possible to reduce suspension movement for small forces (compared to riding over large obstacles at high speeds) like pedaling and braking, but it will also make the suspension more hesitant to move in other situations resulting in less grip or harsh ride. That being said, Fox and Rockshox are trying to use electronics to make suspension a bit smarter so it can detect where the input loads are coming from and decide to open or close the valves.  

So I'd say it makes sense to a certain extent, but from a bike design standpoint, it's better to get the kinematics right and then fine tune the suspension to polish the feel. For example you can take the approach that Neko Mulally has with his dh frame where he decided to use o-chain during the design phase, so he did not have to worry about pedal-kickback. Or you can do switches like Scott or Canyon. Or you can have a good suspension platform that just works like Santa Cruz that does not rely on additional technical measures and keeps things simple.