You may have noticed: pre cut vegetables are not only cut, but also packaged, unlike most fresh vegetables. There is a good reason for this: as soon as vegetable is cut it begins to lose nutrients. Moreover, it is much less resistant to germs.
That loss of nutrients is not in itself such a point: that happens in your kitchen also if you cut your bell pepper for example. The difference, however, is that you usually eat it immediately, while when it is cut in the factory it often takes a while before it ends up on your plate.
In order to avoid a significant loss, food manufacturers take all sorts of measures: from special packaging materials to preservatives. That is not a single objection to health: there are strict legal frameworks for this. And to give you an idea: it is often limited to vitamin C as a preservative and an inert gas (carbon dioxide or nitrogen) instead of air in the pouch. And usually those measures work excellently. In short, in terms of nutrients, pre cut vegetables are very similar to fresh vegetables.
So, pre cut vegetables are just as healthy as fresh vegetables. It contains about the same amount of nutrients and is just as safe to eat.
In practice, there will be other things in play. There is one consideration, which may be much more important than all the stories about vitamins and the like: the convenience factor in relation to the cost picture. Pre cut vegetables are almost always (much) more expensive than uncut fresh vegetables! However, it is much easier and quicker to prepare.