The reasoning seems to be that wooden shafts *can* splinter, and present a risk of severe injury to a horse in an accident. On the less expensive metal carts, the shafts, in my experience, are of fairly thin metal, and *could* bend or even break in an accident; however, there is usually less chance of a bent/even broken, shaft of this kind to do serious injury. Once bent, such shafts would not be safely repairable, and should be replaced.
In higher-end metal carts, the metal of the shafts is generally a good bit heavier, thicker-walled, and therefore, harder to damage in an untoward event. Either type of shaft can generally be replaced and the cart again made usable, as long as the shaft was the ONLY part damaged. Cost , and ease of actually performing a replacement, can vary considerably.
I personally prefer metal. I have an 'original' Frontier EE 'pipe' cart, which is my 'go-to', everyday, vehicle, and has been for MANY years...I've had my current one for @ 15-17 years now; the one I sold to buy this one is still in heavy use as a training cart for the friend I sold it to--I had @ 10-12 years of use on it; sold it only because I liked a newer color scheme better...and, the back of the backrest had been 'chewed' by horses I'd led while driving it! I also have a Bennington(made in the UK) that is my all-time favorite cart. It is all-metal except for the seat base; the shafts are of aluminum, heavy-wall, w/ a 'rubbery' black coating; it is a considerably higher-quality cart. I also have an all-wooden cart, from a well-known maker, and of high quality. It is 'prettier' than the metal carts, I guess, and rides well, as does the 'Benny', but I don't use it because I prefer the 'Benny'.
Overall, the weight of the higher-end wooden AND the better metal carts is often very comparable; in mini horse size, tends to hit at about 110-120 lbs.
Edited to add, in response to the post above: I have never noticed a problem with any of my harnesses related to the diameter of the shafts. Mine are all high quality harness, however...even my 'everyday' training harness is a Smuckers 'Lite'( in russet leather). I have used Tilbury tugs(on my Lutke show harnesses), wrapstrap, and open tugs w/ a holddown strap-type harnesses; no issues w/ any of these. It IS generally true that wooden shafts will be of a larger diameter than most metal ones...though on the Benny, the aluminum IS of a larger diameter and thicker walls. I have encountered metal carts w/ solid steel rod, of smaller diameter, for the shafts, and ones w/ heavy-walled, small-diameter, steel pipe for the shafts...but none were a problem. If using wrap straps or Tilbury tugs, the material needs to be flexible(one possible 'problem' w/ bio or beta-bio harness; the strapping material *can be* stiff...) You may indeed need tug stops on the shafts, and those could be harder to install(yourself) on metal shafts.
Margo