For training athletes, I agree 100% that more simple movements are better. There's no debate; the olympic lifts are hard to learn and this takes time. Athletes in sports like football, rugby or whatever will gain more benefit from exercises that don't take long to learn. Removing the limiting factor of 'skill necessary to correctly perform the lift' means that you can ramp the weight up to where 'pure strength' becomes the limiting factor and thus gives you a training effect.
As to whether one style is better than the other in general terms, I agree with Garrett, it is a pointless debate. Why not use both? It obviously depends on your goals. Ultimately the body doesn't know whether it has to lift a barbell, a tyre or anything else. Explosive contraction is trained regardless.
I like variety in my training because my sport is crossfit, so I try to make use of strongman, olympic lifting, powerlifting, gymnastics etc to give me broader athleticism. So for me it is about choosing the movements that I feel will give me most carry-over to all other disciplines. Doing the olympic lifts will make me stronger at the olympic lifts and also benefit strongman and crossfit. Doing strongman will make me better at strongman and crossfit, but is less likely to improve my olympic lifts.
It makes sense for me to perform the high-skill movements often, as I get carry over to other things. Strongman, powerlifting etc is good for variety and to increase all-out strength, but if I can potentially realise improvement in these without training them, I then have more time to train other exercises (which require more practice, such as the olympic lifts).
Likewise, gymnastics are likely to improve other aspects of fitness due to the incredible strength they build. But you just aren't going to get good at gymnastics without training it.
So it seems logical, to me at least, that you perform the exercises which give you greatest carry-over to ALL other things, as well as that thing itself.
Does that make sense?