Either way it depends on your cart or carriage and what class you're showing in, Western, Country, or Please.
And whether you're showing AMHA/R, ADS, parades, draft exhibitions...all sorts of things! Collar and hames are only appropriate with a vehicle that has a low singletree (around the level of the hocks, not up above the shafts) and are the only appropriate choice for draft-type work where the horse is pulling against a heavy stationary load. Advantage: best possible distribution of load, correct ergonomic angle for heavy pulling, frees the shoulder. Disadvantages: Absolutely MUST be correctly fitted or can easily sore the horse. Not appropriate for a horizontal line of draft.
Breastcollars are correctly used with road carts, show carts and other vehicles with straight shafts and a horizontal line of draft. They work well for a vehicle that is going to be rolling easily across level ground. Disadvantage: Not good for pulling a lot of weight. If you use it with a lowered singletree a lot of pressure can be put on the neckstrap and cause discomfort.
There are quite a few options in between these days, at least for minis.
There's the Deep V collar from the Carriage House and similar models from Ozark and other vendors:
Depending on your horse's conformation they can be helpful. The advantage is they give more room for the windpipe, the disadvantage is that they may not be built to fit your particular horse properly and can actually sit
lower on the front of the horse's shoulder than a straight breastcollar in some cases. I've seen it!
Camptown Harness and Chimacum Tack sell a Freedom Collar which works for both horizontal and lowered draft because it has a ring attachment for the trace instead of a sewn-in, set angle.
This collar is MUCH more shaped and clears the shoulder quite easily even on a horse with a very low windpipe like Kody. It is nicely padded for good weight distribution but the straps don't attach in such a way as to distribute the weight up the shoulder blade like a neck collar would. Used on anything but a horizontal draft vehicle it can put significant weight on the neck strap unless the horse has a very high neck set allowing the collar to sit tipped down already.
There's the French or Eurocollar, which is a combination of a neck collar and breastcollar.
Again, this works best on a horse with a high neck set like the Hackney it's pictured on. To me this collar is too bulky, too wide in front, and made of leather that is too hard. I don't like the way it covers the point of the shoulder on most horses but I do like the way it has a thick piece up along the shoulder and across the neck instead of thin straps.
Breeana Sheahan (Minihgal) uses a creation of Tanglewood Miniatures called the "Californian Soft Collar" (I've got one on the way, hope to have it by Happ's!) which is basically a Eurocollar but is customized for each horse and offers different angles of draft at your request. I feel this one is better because it's made of softer leather, doesn't cover the entire chest as the Eurocollar does, and is lighter overall. It improves the distribution of weight and the ergonomic angle of pull over a breastcollar without the bulk of a neck collar.
It really depends on what you want for your horse and how they are built. What works for one horse will not be comfortable for another. Can you tell us more about what you're pondering?
Leia