We are building a 4x6 shower in our master bath..I want a rain shower head and a handheld shower head that both can run at the same time. And the handheld shower mounted on a bar. And not get scalded.

I found a Moen set at Faucetdirect that looks nice and is inexpensive but when I add it to the cart, it says I need an additional $382 part.
Moen shower

A more expensive Hansgrohe system says that the extra part is only $80. hansgrohe shower

Why such a difference? Which is better? Any other suggestions?

The second selection process then has you buying the brass valve body or valve bodies that do the actual temperature control, or do the actual diverting of the water to the shower heads.

Both trim kits are expensive. They usually are when you get into multiple shower heads, wall bars, and valve controls.

The shower valve itself that goes inside the wall, which is what you are purchasing in the second step on that website? The Hansgrohe set has a SINGLE valve inside the wall, whereas the Moen setup needs THREE valve bodies.

Valve bodies and trim sets need to be matched to one another. But once you choose that valve body and trim kit that fits that valve body, you can use pretty much any shower head or heads with that valve. Sure you'd want to make sure the styles and finishes coordinate. But you can shop freely. You pick a valve body that will do what you want it to do:
-control water temperature
-act as a volume control
-act as a diverter to send water to just the shower head, OR to just the handheld, OR to both at the same time

Some companies make a single valve that can do all that. Other companies, you need several valve to do all that.

Fewer parts usually means less money.

As an example, a SINGLE valve that can do everything you want would be the Hansgrohe Thermobalance III valve. It's affordable too.

If you were to buy that Hansgrohe TBIII valve, then you'd need a Hansgrohe trim kit that fits that specific valve. But then you can use a Hansgrohe rainshower head or any other manufacturer's rainshower head. And you can use a Hansgrohe handheld on a bar or any other manufacturer's handheld on a bar.

If that's confusing, you may find clarity or even more confusion here.

Good luck with your search!

The second selection process then has you buying the brass valve body or valve bodies that do the actual temperature control, or do the actual diverting of the water to the shower heads.

Both trim kits are expensive. They usually are when you get into multiple shower heads, wall bars, and valve controls.

The shower valve itself that goes inside the wall, which is what you are purchasing in the second step on that website? The Hansgrohe set has a SINGLE valve inside the wall, whereas the Moen setup needs THREE valve bodies.

Valve bodies and trim sets need to be matched to one another. But once you choose that valve body and trim kit that fits that valve body, you can use pretty much any shower head or heads with that valve. Sure you'd want to make sure the styles and finishes coordinate. But you can shop freely. You pick a valve body that will do what you want it to do:
-control water temperature
-act as a volume control
-act as a diverter to send water to just the shower head, OR to just the handheld, OR to both at the same time

Some companies make a single valve that can do all that. Other companies, you need several valve to do all that.

Fewer parts usually means less money.

As an example, a SINGLE valve that can do everything you want would be the Hansgrohe Thermobalance III valve. It's affordable too.

If you were to buy that Hansgrohe TBIII valve, then you'd need a Hansgrohe trim kit that fits that specific valve. But then you can use a Hansgrohe rainshower head or any other manufacturer's rainshower head. And you can use a Hansgrohe handheld on a bar or any other manufacturer's handheld on a bar.

If that's confusing, you may find clarity or even more confusion here.

Good luck with your search!

So if I like the look of the Hansgrohe trim kit, is the iBox 3/4" valve a good one or should I look for one that takes the Thermobalance III valve? Or do all Hansgrohe shower trim kits take all the Hansgrohe valves? And in that case what's the difference between the iBox and the Thermobalance III?

And for my son's bathroom and the guest bathroom, is there a quality difference between the different brands of valves? I will probably go with pressure balanced for these locations, and I don't want to spend a lot. But I assume I don't want to skimp on the valve if it's going to be buried in the wall and difficult to replace down the line, unlike the shower head, right?

"Out of the box" the iBox valve is only an A OR B diverter. It can't send water to BOTH heads simultaneously. When you install the valve, you'll need to remove a small rotation limiting clip (I don't recall the exact name of the clip) on the valve that limits the rotation of the diverter valve. With that clip removed you can fully rotate the diverter valve to an AB position and water will flow out of both heads simultaneously. They probably have instructions for that in the installation manual.

So to make things easy, yes, you can stick with the 3/4" iBox, just remove that diverter limiting clip when the valve is installed.

For your other baths, if you want to stick with Hansgrohe, their pressure balanced valves are around $75 and the trim kits for those valves are another $125-$500 for a valve trim kit and a coordinating shower head and tub spigot.

If you're looking for economy, I usually recommend the Symmons Temptrol pressure-balanced valve. They aren't the prettiest ones out there, but you can buy a complete setup (the rough valve body PLUS trim kit PLUS a shower head and tub spigot) for about $90-$100 total. The valves are excellent, they have been around forever, and they are well supported. The few times I've needed a replacement part Symmons sends them out for free.

A lot of folk will install the Symmons set, then later maybe spend a few dollars and replace the shower head that came with the Symmons kit with one they like better.