I have braised in the oven, and slow cooker both. The difference is in temperature control. A typical oven has temperature ranges between 170' F (76.6' C) to 500' F (260' C). This allows you to control the braising temperature. A slow cooker has three heat settings, warm, which keeps food at about 145' F (62.8' C), low, which is a slow simmer, or high - medium boil). Water boils at 100' C, which can overcook meats, and dry them out. So if braising in the slow cooker, cook on low to avoid that, and get that pull-apart, tender, moist meat you are looking for. Trust me on this. I once put some meat in the slow cooker, covered in braising liquid, set on high, covered it, and let it cook all night while I slept. I checked my roast the next morning. It was still covered in liquid. I was expecting something wonderful. What I got was very tough, dry meat.
As meat is heated past 145'F (62.7' C), the proteins begin to contract, squeezing out juices, and becoming more resilient (tougher). Interestingly, a piece of meat that has significant fat marbling, collagen, and gristle, cooked for 30 minutes or more between 190; F. (87.8' C), and 210' F (98.9' C) actually becomes more tender and flavorful as the fat, collagen, and gristle melt, and soften.
So, depending on the meat marbling, the amount of fat and gristle, adjust the braising temperature to get the best results. Whether you use the oven, or slow cooker, the flavor will be the same. Heat is heat. Where it comes from doesn't matter. Both your Dutch oven, and slow cooker insert are ceramic, and so will not affect the flavor. The only caveat here is that all of the Dutch oven will be at the same temperature, while the slow cooker insert is heated by a band that surrounds it, giving you a hot spot right around the middle of the sides. For your roast, this won't be a problem. For sauces, chili, and stews, this can cause burning, or over cooking at that hotter section, and so the need to be stirred every 15 to 20 minutes to avoid that issue.
Hope this helps. Seeeeya; Chief Longwind of the North