yes and no
for the most part all smart pots root prune.....
some root prune because of root contact with air, others with chemicals in cloth, and others limit size of root escaping pot.
I doubt burlap would control outward root growth like the smat(er) pots.
I have much experience with rootmaker and super root pots. aka air pots (air prune), and have had great results.
I have a few "spin out" bags, which are essentially felt bags coated with copper hydroxide coating. I don't think the air/water circulation with these bags are as good as "air" pots. but the growth verdict is still out.
i cannot attest to cone shaped pots, but i like what the the rootmaker multi cell to 3inch pots do for small stater plants. I do have experience with rootmaker grounder (5 gal), but only above ground, i think this pot is best in ground. ....It is cone shaped....i this what you are referring to?
rootmaker makes a net fabric bag, which im anxious to test because you get the best of both worlds, (not to mention cost effective) allows for air pruning and allows for escape rooting from bottom. I'm currently trying to get my rootmakers to root out bottom of pot, to get the best of both worlds. the net fabric essential chokes root allowing only smaller roots out ........
also there are more varieties of smart(er) pots with different technology/and grow theories than you have listed.
I think any of the air pots are superior to standard nursery pots. although there is science that begs to differ with regards to top growth. But for our goals definitely superior.
the key to these pots are controlling the: soil mix, watering and feeding, to the trees needs to get maximum growth.
i hate to challenge dogma "why the earth is not a pot", but air pots do challenge this science.
So to ultimately answer your questions "My question would be is there a type that works best? And do the three types differ or are they just different means to an end?"
It all depends on your resources and goals for which is best. i've seen air pots sell for over $8 each. you have to custom mix soil to watering habits and tree needs and type of pot. so given that there is no best. however i am partial to the hard sided, rootmaker/ air pruning type pot, secondly the net fabric bag.
yes they do differ, but in the end produce stronger trees with better root systems.