Why use a weightlifting shoe? For exercises that require a full range squat pattern the heel elevation allows greater range of motion by placing the shins angled forward in relation to the foot (more dorsi flexion). In turn this allows the centre of mass to be balanced over the mid foot with a more upright torso position, minimising the risk to the spine. The mid-foot strap provides stability and reduces pronation (rolling in) of the foot. They should also have a very solid sole with good grip in order to waste as little force as possible when lifting.
The Adi-powers (right in pic) are my favourite for the full olympic lifts (snatch/clean and jerk) as they feel the most secure and rigid. *Update* I now have a pair on the newest Adidas LEISTUNG 16 II SHOES which I'll review as soon as I've worn them for a training session.
I got the Asics lifters (middle in pic) as I had never seen them before and knowing Asics have a decent pedigree in old lifting shoes thought they'd be great. They're not. The sizing is weird (international sizing doesn't match up) and the strap is built into the upper but only halfway down so feels less effective and not hugely comfortable. Fine for just squatting in but I won't do jerks as they slip off at the heel. After trying them out I read that they're an attempt at a hybrid lifting shoe (one that can be used for cross-training not only weightlifting). I think this makes sense but that Asics have missed the mark a little with this one, reflected in not doing much promotion unlike the other brands possibly?
The inov8 fastlift 325's were on sale so I couldn't resist - even though they're really a hybrid (and crossfit) shoe they do feel very comfortable and light. Good for snatching in. They have less arch support than the adidas and being very light do feel less stable. This would be my go-to pair for travelling as they're so light and allow a wider variety of movements. I'd just steer clear of them on heavy/ max attempt days.
Next I'll try and get my hands on some Nike Romaleos, Antas and the newest version of the Do-wins to see what difference they make to my substandard lifting!