Is bolognese better cooked with the meats being seared or just simply sweat without being seared? Some recipes I have seen just sweat the meat then inserts the vegetables in them (so the meat is gray colored), but some recipes say you have to have them browned to have the maillard reaction give extra flavors. 

I have watched several youtube videos regarding Bolognese recipes and all have different styles.
"Better" is a matter of opinion.  Recipes for bolognese vary widely. Both methods are possible.  Try it both ways, see which one you prefer.  My practice is that the meat is not seared.  Because of the nature of the recipe, I usually have a lot of meat, it would certainly take longer to sear it in batches, as opposed to dumping it all in with the sweated vegetables.