If you stick with white trims, most come pre-finished.

Woodwork is in every single room of your home so it will make a huge impact. There are folks who like stained and those who like painted. They usually don't like either one or the other. The choice is yours. Look at pictures on HOUZZ and see which person you are. You won't be sorry to take the time to do that- it is definitely worth the expense for those of us that like painted!

I like the looks of painted trim too...stained trim...makes it difficult to make changes later on down the line.

I like painted trim. When our house was built 10 years ago, stained trim was definitely an upgrade as Sophie described.

I think the difference is pretty clear. When you want to change the color of painted trim....you paint it. When you want to change the color of stained trim, at the very least, you sand it, stain it, and varnish it. There is a stain, varnish treatment in one can, yes. But there is still a lot more work to change the color of stained wood. Also you are pretty much committed to having all the woodwork on one floor the same color. If you go with a stained stairway you might even have to make the whole house that color.
Why would you stain? If you have a particular style in mind for your house and do not intend to change it anytime soon, then a stain might work for you. One warning, your typical builder grade woodwork looks really poor when it is stained. To really make stain work you need wider woodwork with some detailing. BTW I have that kind of detailed woodwork and still painted it.

Generally speaking your contractor is correct. Painted is more expensive than stained.

Stained pine looks awful. If it's not a quality wood, don't do it.

painted interior trim is cheaper as it usually uses cheaper woods like poplar. Stained wood has to generally use a better and thus more $ wood - pine is one of the less expensive and then you go up from there.
Painted offers more numerous millwork options over stained. Stained wood does offer millwork options, just not as many. Both paint and stained offer numerous paint colors or stain shades. Pine for instance does not mean an orange or rust color.

But there are today's trends - to paint or to stain, so like others have said make a choice based on what you like.

One option.. Use stained in the primary rooms (living room, dining room, foyer, study) and painted trim in the less visible room like utility, bathrooms, closets, or where you want a specific style or color or you are on a budget.

Another.. painted can make a room like larger or brighter like a sun room.

Stained is warmer and can provide great focus wall colors or enrich walls, albeit painted millwork can create a great statement because of wonderful detail.

Not sure what your builder is talking about when he says you don't need to fill and sand stained wood...or put on multiple coats. Depending on the wood, a sanding sealer is laid on, then sanded. The stain is applied in one or two coats and let dry. Then a coat of clear varnish or waterborne urethane. Sand again. Then color matched putty...individually tinted by hand to match the grain, filling all the nail holes. Then another coat of varnish...or two, sanding in between. No caulk. In my trade we have a saying..."a little caulk, a little paint make a carpenter what he ain't." Only the best finishing carpenters do stain grade work. Paint grade is for rookies and hacks...or for budget...or style. Paint grade done to stain grade carpentry makes my painter happy. He spends less on caulk and his fingers don't hurt at the end of the day.