For a very obvious reason, run them both on the same tyres and you will feel it.
But no one conveniently sells all these different bikes with identical tyres, so that's a moot observation.
The point is they're all different, but more often than not it isn't marked. In fact, jn my experience of all the the biggest attributes are negative, and apply to the 29er:
1. Bigger wheels are flexier, noticeably so for a heavy rider. Like for like, you need to spend more to get equally decent wheels.
2. Bigger frames aren't as stiff, particularly at the rear. Again, highlighted by me being a heavier rider, managing to make a Boardman 29 frame flex so much I could make the rear tyre brush the frame on the power stroke.
3. 29ers are a nightmare muddy conditions. as the extra circumference provides additional surface area for a couple of extra kilos of mud to stick to, very, very noticeable over a 26.
But that aside, none of them inherently do any one thing so much better than the other that the losers have become obsolete. The 26 climbs a wee bit more lively, the 29 descends more steadily. The 29 rolls a touch better (although always having owned road bikes as well I've never felt the way in which they roll was revelatory), but the 26 gets up to speed with more snap. Unsurprisingly, the 27.5 is largely in the middle. Ultimately they all get me round my rides with aplomb.
Nevertheless, my ride times are much the same no matter which of my 5 MTBs I plump for, suggesting that the biggest difference is in feel. That leaves taste and preference as the decider.