American 666s have, obviously, high FP, excellent range, good broken morale, and a high smoke exponent. So all that's been said before is good. I'll just add two things.
Because they have Assault Fire, trying for Smoke during the MPh is not such a big loss compared to Prep Fire: a 666 will have 4FP in the AFPh, only losing 2 compared to the PFPh; so if you try for Smoke before moving and get none, or even roll a 6 and don't get to move at all, you can still be effective in the AFPh. Of course, laying Smoke in an adjacent Open Ground hex and then moving into it can't be done with Assault Movement (but if you declare AM and manage to lay Smoke, you can declare a late CX to still spend the next 2MF to move into the smoke - that way you don't get the CX penalty to the Smoke dr, and if you fail the dr, don't get the CX).
Also, because they have high broken morale, getting broken is not such a big deal for them - you just rout away and come back. Of course making sure you have a valid rout path is essential - even more so than with 7 Morale troops, because they do break easily. But perhaps paradoxically, it's sometimes a valid move to have a 666 move into the open to draw fire from an adjacent unit - it's likely to break as a result, but your other units will then be able to move more easily. Just make sure you have a valid rout path, and check that you have a good ELR - those 546 are not as good as 666.
Oh, and when you need to attack in not so good TEM terrain, you'll often be able to build "amoebas" - large multi-hex fire groups. Your guys have low morale, so spread them out so that a single defensive shot will only harm one unit, and blast away in the AFPh. Your leaders should then stay behind for rally duty.