If bikes from different brands have essentially the same geometry and similar kinematics - even if they have a different suspension configuration - they may feel very similar. Shock tune could still play a role, though.
Sometimes bikes from the same brand feel very different. For example, the previous generation of Specialized Enduro had old-school geometry, a fairly flat motion ratio curve, and low pedaling anti-squat. The new generation has much more modern geometry, a fairly progressive motion ratio curve, and high pedaling anti-squat. Totally different bikes.
In other cases, one bike may focus on light weight, while another may focus on being extremely stout. You'll probably feel the difference in frame flex - and flex isn't necessarily a bad thing - on bikes at opposite ends of the stiffness spectrum, but probably not between bikes clustered around the middle.
The bikes you mentioned (assuming we look at the Trance X, rather than the Trance) are very much clustered around the middle of the bell curve. Geometries are similar, kinematics are similar, weights of the carbon frames are similar, stiffnesses are similar. I've been told the aluminum Stumpjumper frame is heavy, but haven't verified that for myself - and it would probably be only a pound or so, which is maybe 0.5% of the total system weight. They're all excellent "trail" category bikes and they're all very similar. Choose the one with the best value or even your favourite paint colour!
I can feel a difference between two of the same bikes set up differently, and definitely between brands as there are several factors to consider when comparing bikes.
I can feel a difference between two of the same bikes set up differently
That's a valuable statement for putting things in perspective. A few changes in set-up for a given bike can be more significant than the differences between bikes. It's less useful to chase the "perfect" bike and be casual with one's set-up of that "perfect" bike than to choose a good bike and really dial in the set-up.
Besides actual performance, one difference I can definitely feel is reliability. I had a Bird for an year, zero issues. Then on a Specialized Stumpjumper Evo for another year and the damn bike was falling apart. Bent shock bolts, creaking everywhere, knackered bearings etc. Now again on a Bird since July, perfect