The adjustable (windage only) sight on the Laramie is a nearly exact reproduction of the original "target" sight S&W made available for their New Model No. 3 "back in the day."
Unlike the SAA, whose barrel can be (and frequently is) rotated slightly to correct windage problems, no such adjustment is possible with the break-top revolvers. IMHO, it is very short-sighted of SASS not to permit these revolvers to compete against the SAA style that have often had their barrels "turned" to correct windage.
Alas, however, that is for SASS to decide.
The Laramie IS permitted in NCOWS competition.
The Schofield does NOT have the driftable rear sight therefore 1) It is SASS legal and 2) you take your chances on correct windage or "kentucky windage" if necessary.
IMHO also, the Schofields are usually pretty well right-on windage-wise.
The other main difference between the two is in the grip shape. I have owned both (no longer have any Schofields) and never was totally comfortable with the Schofield grip (it's all about personal preference). On the other hand, the Laramie (NM#3) grip feels perfect in my paw. It is so close to the NM#3 grip shape that repro NM#3 grips will fit the Laramie with very little fitting.
Both are fine guns, but the Laramie is far superior TO ME due to grip shape, balance and overall looks.
JMHO. Hope it helps.