Toilets, Sinks, Showers, Tubs and Disposals - making new ensuite shower: cement base or concrete boards first?

I am doing reno in ensuite including making a fairly big glass - on two walls - shower. Drywaller says cement base should be poured first. Tiler says boards go up first and should be brought almost to the bottom of the base (so that the sides would be sealed after the cement base is poured). Can someone tell me if there is a right and wrong way or if either way has it's own merits? (I am losing faith in my tiling contractor since most people I talk to say the base should be poured first!) Thanks in advance.

rip out existing walls to the studs. - tie in 2X12's between the joists at the base for framing - set your plumbing - pour your base (properly done is a multi step process with about 6 layers - tar paper/metal lath/mud/liner/mud/lath/mud) - install your CBU (not drywall) within 1/4inch of your new base - caulk well - install tile....

Thanks Zster. (I'll pass on the 9 a.m. beer but an Irish coffee would be great!) Is there any way possible that the CBU goes on first? That the cement can be poured after the concrete boards are in place? (My drywaller is coming in 3 minutes!!)

here's a new twist. NO, my shower is still not completed. 16" ceramic tiles are being used and they look great. BUT, as I expected, there is no way to install this size tile on base and have it looking good. I am meeting contractor in 3 hours (8:30 pacific time). MY original suggestion was to do a terrazo style floor or insert small decorative pieces into the cement when it was poured but I was assured there would be no problem in using the same tiles as are on the walls! Any suggestions on how to get a concave floor with this size large and, of course, flat tiles?