I’m not exactly sure what you are asking, and the question is too vague to give a concrete answer. For starters, the massive geometry differences between bikes of the 26” era and those of the 29” era will have much more of an effect than the change in wheel size.

@MaplePanda In the video accompanying Michael Jackson's "Black and White" (youtu.be/pTFE8cirkdQ?t=331), people of various ethnicities are morphed to one another. Suppose you are looking at someone riding a 26″ bike. Now the bike is morphing to the shape of a 29″ bike. As an observer of this morphing operation, can you identify two or three characteristics that have changed in the rider's position?

Is the cyclist pedaling at near the speed of light?

In other words, what are the differences between frames build around 26" and 29" wheels? It would be hard to separate the effect of bigger wheels from the decade+ of design progress.

@Criggie 1/2 Think of an Amsterdam cyclist, riding in a very comfortable posture. Even if I take the video and edit out the bike, by just looking at the cyclist you immediately recognize the bike they're on. Think now of a cyclist 500 m before the end of a TdF stage (but not 100 m, when everyone's off the saddle). Just the video of the cyclist, without the bike, tells you they're aggressively riding a road bike.

@Criggie 2/2 What would you do to morph the Amsterdam cyclist to the TdF one? I'll take a stab: 1- the back goes from upright to near horizontal, 2- the saddle is raised to near the highest that it can go without the cyclist rocking, 3- the elbows are bent from near straight to almost perpendicular, etc. What are the signature changes in posture for a rider from a 26″ to a 29″ bike?

@Criggie It's the other way! Let's completely ignore that the bike has changed (you're right; the differences would be tough to pinpoint, partly because they may not even be the same from one manufacturer to the other). Let's look at just the cyclist. What changes are there in the cyclist's posture? (It's possible that there aren't any.)

I think you're missing the point still. The cyclist's posture changes, yes, but it has more to do with the geometry updates than the wheel size difference, and it all fluctuates so wildly that nobody can really answer properly. To summarize: reach has grown by like 80mm in all sizes, stack has increased, BB height has increased, seat tube angles have steepened by 3-4*, bars have widened by 50mm, cranks have shortened, bars are now higher than saddles...but I don't see the point of the question either. What knowledge are you gaining?

@MaplePanda Say I see someone riding fast, but not sprinting, on a 29er on a forest trail. I comment "How odd! This posture reminds me of a horseback rider galloping. It doesn't particularly look like someone riding a mountain bike." Then you would comment "Ah, yes, but that's because of the adjustments made to modern mountain bike frames of all ilks, not just to 29ers. All postures, whether on 26 or 29, are now elongated and aggressive even at lower speeds." Is that what you mean?

@whatsisname for realistic cycling situations, I believe the first questions are whether we can assume that the cyclist is spherical and in vacuum

Do you realize that bikes with 16" wheels are frequently built with geometries (for handlebars/pedal/seat positioning) matched to bicycles with 26" or 29" wheels? (This is a service that Bike Friday offers for their custom-frame foldable bikes). Wheel size is not destiny.

@CharlesDuffy I am not entirely clear on your point. Please elaborate. Anyway, I'm asking a question, and you're replying with a question. Ideally, please just write an answer with your observations. If you're able to include a picture of the resulting geometry you discuss, that will be ideal.

@Sam to me it looks like you wrote a whole lot of confusing misinformation and are now debating it instead of focusing on the question.

...however, to elaborate briefly: One can build a bike with smaller wheels with the exact same rider positioning as a bike with larger wheels, so the question's premise (that different wheel sizes must force changes in rider positioning) is inherently false. For a company that makes bikes doing exactly this, see bikefriday.com

@CharlesDuffy The point is that either you are or are not making a contribution to the question/answer. If you are, your contribution will never be found among comments by future readers, and this site is not for the service of just those who ask, but all those who seek. Your thoughts are hence solicited either as an edit to Nathan's (nice) answer, or as an independent answer that cites his answer and points to additional details.

I think a much more answerable question would be something along the lines of "how and why has mountain bike geometry changed over the past x decades?" Then you can really get into the positioning differences without being constrained by wheelsize instead of having wheelsize be a supporting point.

@MaplePanda Re: "a much more answerable question": That's a nice question for bike designers, but I ask this question from the perspective of a cyclist looking at postures in a mirror.

So, is the real question "How do I read frame geometry tables so that I won't order wrong size of frame again?"

@Sam What bike? I can confidently say that the difference in feel is because of the ~80mm longer reach, taller stack, wider bars, massively increased wheelbase, steeper STA...all of which are parameters only remotely connected to wheelsize. 26" bikes were generally made before this "long, low, slack" revolution. It's not the wheelsize change which drove this geometry change, as Charles points out. Nowadays, we have medium bikes with 460mm reach, a number you would have seen on an extra large a decade or two ago.

What is 27.5? Is it 700c (i.e. 622 mm)?