PLA is hard and rigid but is also brittle. That means it has little elastic deformation before breaking (simple test is to bend the filament). So if you construct something where the tolerances are too high, forcing the PLA in might cause it to break or it won’t have the ability to “squeeze” in. Not really the best material for push fit.
ABS is not as hard as PLA but has a larger elastic zone before failing, i.e. it’s stress strain curve is steeper. To further illustrate this and trying my best not to use too many technical terms…
Referring to the image stolen from Wu et al. 2015 below, the horizontal axis is the elongation and vertical axis is the force required for that particular elongation. The end of the curves are for when it breaks. Comparing PEEK and ABS, ABS’s stress strain curve is steeper.
Here you see PEEK failing at about 60 MPa @0.09% elongation
ABS fails at about the same elongation but at 30 MPa.
In simple terms if you were to have two identical push fit parts with the above materials, assuming the same geometrical accuracies, both will fit but you need to push twice as hard for PEEK. So it depends how tight you want your parts to fit and whether you want to push it in by hand or with the help of tools? How high the force is also depends on your contact area and sizing.
The curve for PLA will be less steep (more vertical) meaning it will have less change in elongation and just snaps once you reach a certain stress.
TPU’s curve is verrry steep (leaning towards the horizontal axis), so you can push it in easily but it also falls out easily (ok this also depends on the compression… but this is the general idea). This doesn’t mean it’s bad, it just depends on your application.