The difference between a "continental" shoot or a driven shoot (which the continental is supposed to replicate, although driven birds are usually better fliers because they've been out and about for weeks or even months by the time they're shot) and our typical walk-up hunting for wild birds over dogs is that most of our shots are at some sort of outgoing angle. Trap really isn't bad practice for wild pheasants, because unless you're a blocker at the end of a field drive, you're going to get mostly trap-like shots. Within 30 yards or so, most of those birds can be taken with 7 1/2's, the main problem being that you end up with a lot of pellets in the meat. 6's will get you to 40 yards. 5's and 4's become necessary if you're going to take many shots farther out than that--although a lot of pheasant hunters aren't good enough shots to make use of the larger shot because it also requires a tighter choke if we're talking 40 yards +, and the tighter choke will handicap them on the closer birds they're more likely to hit. I've killed more with 6's than anything else; quite a few with British 6's or US 7's, some with 7 1/2's, and some with 5's--typically late season when the birds are all full grown, packing fat to protect them from the cold, and shots can be longer. I've never used anything larger than 5's. But I've also done most of my pheasant hunting over good dogs--the best of which, over a span of 6 seasons, recovered 491 birds shot by me and those hunting with us, while losing only 12. Those who are better shots than I am, and maybe don't have dogs with quite the experience, might well make good use of more choke and larger shot than I do.
The Brits, who more or less invented driven shooting, traditionally use what most American pheasant hunters would consider light loads of shot that's on the small side. The standard choice is British 6, which is slightly larger than our 7's (about 6 2/3). It's mostly a 12ga game, but shot charges are usually an ounce or 1 1/16, sometimes 1 1/8. Those loads work quite well on "typical" driven shoots, where a 40 yard bird is a high one, and the average height is almost certainly under 30 yards. That's the game for which the standard British game gun (2 1/2" 12 weighing 6 1/4-6 3/4#) was designed. And it's as effective today as it ever was.
There's a subset of that game for those who prefer much higher birds. That game requires special terrain--hills, trees, and valleys--in order to offer a consistent diet of 50 yard + shots, with plenty of birds higher than that. Those people mostly shoot OU's like those we see at sporting clays shoots: barrels 30-34", weight upwards of 8#, loads in the vicinity of 1 1/2 oz, through tight chokes.
For those who might be tempted to try a driven shoot for the very high birds, I'd recommend experiencing just your standard garden variety first. Those birds can be plenty challenging. Or at least they are for me.
