Normally all trim and doors are finished the same throughout a house, this creates uniformity.
If you stain the trim then the doors should be stained as well. This does look really good. I have stained doors that have painted trim and was surprised by how good this looks, but I have not seen the opposite.
Having painted doors with stained trim will make the doors stand out more. If this is the look you are after then go for it. In the end it is what you want that makes the most sense.
Another consideration is the extra cost of a stain grade door vs a paint grade 6 panel (standard type of door). This is a considerable difference.