For any harness you get, make sure there is a tree in the saddle. This keeps harness and possible shaft weight up off the animal spine. Just like a riding saddle, there should not be weight on his spine doing his work.
Most folks love the synthetics, so much easier to care for. We do carriage driving, where the matte finish seems to be very popular. However the minis, horse folks who do ring classes with fine harness (type shown above with mini) often like the shiny biothane finish better. More flash and sparkle! I have not heard of stretching problems, but synthetics do wear differently than leather. Some parts are made to be replaced regularly, like billets with lots of pressure on them. Girth billets, rein billets, hold back straps if you use a breeching. If a hole gets ripped, get things fixed promptly for YOUR safety.
Check for good quality hardware in your buckles, get large rein rings on the saddle so a twist won't snag running thru on turns. Buckle tongues should all be steel, NEVER brass tongues on a buckle. Brass is pretty, but very soft, will bend or break under stress that doesn't bother steel.
I have to say I NEVER want my harness parts to fail. Those kind of parts will break when you MOST need them to hold and be strong. Failure of parts can CAUSE wrecks. If an accident happens, I WANT harness to hold, NO FAILURE, to cause a worse problem as horse "thinks" give of breaking part means he can escape. 99% of time breaking parts make it much worse in a wreck.
Properly measure your animal so you can give harness person correct dimensions, for proper sizing and fitting new harness to YOUR pony. Send back parts that do not fit correctly. I find that ordering harness from a maker is usually the most cost effective, comfortable to animal. This is getting animal the best fit of harness, with little difference in cost between a box harness or custom sized. There are LOTS of harness makers who would love your business.