See if this answer makes sense. And I haven't used a pellet grill, so you have to adapt the ideas to your situation.
"Barbecue," what most folks mean by it, is an indirect heat method of low temperatures and smoke. This is opposed to "grilling" which is a direct heat method at high temperature, as high as 500F. With barbecue, the surface of the meat absorbs smoke to a depth of something like a quarter-inch, a very visible smoke line when it's cut. Grilled meat has a crusty caramelized surface and development of flavor from the Maillard reaction, which requires at least 310F. That doesn't happen in barbecuing, because the temperature is under 300F.
Now, starting with those two distinct traditional methods, what's ultimately true is that the right method it whatever works, meaning you get the results you want. You can already see why the flavor is different in your two examples, with one temperature above and one below the threshold for the reaction that's expected in grilling. When barbecuing, the smoke contributes the distinct (and different from grilling) flavor effect. I consider pork one of the meats where a combination of methods is useful, if you like the smoke flavor but miss the rich crust.
If I understand the design of most pellet grills, it might be difficult to begin with high direct heat and transition to indirect low heat. On a charcoal grill, I would begin with coals under the meat for browning and rake them aside for indirect barbecuing at low temperature. But you might have to brown the pork on the stove first, if you want that surface. I don't know if you can get that kind of rapid temperature response with a pellet grill. But you get the idea and maybe why you're missing the old flavor.
Keep in mind that the early browning does NOT "seal in the juices." So, during the indirect cooking, you might consider using a drip pan under the meat and mopping the juices over it from time to time or mopping it with a broth made from trimmings or from a can.
"Kitchen duty is awarded only to those of manifest excellence..." - The Master, Dogen