They just apply pressure across the parallel faces of the clamping surfaces and this is often larger and longer than other styles of clamps whilst maintaining that parallel aspect relative to the clamp and material. In reality you could probably achieve the same result with other clamps and adaptive / additional hardware but often it's the compactness, light weight and ability to lie flat on a surface or against it that gives parallel bar clamps the edge. If that makes any sense?
Sash clamps would be ideal for doors which is why I think people suggested them but as above depends on the thickness of the material overall.
Rutlands' parallel clamps had a bad rep at one point as over time the main metal spine would wear and lose grip. It only came up on the forums as strangely none of the real reviews appeared on Rutlands' website (I'm sure that was a one off for Rutlands!!!). Not all clamps, even identical looking ones are built the same with the same standard of materials and to the same level of QC or indeed recourse if they fail. Rutlands will have almost certainly just outsourced a supplier for their current clamps with clearly a deal to put their name on it, that said this isn't necessarily a negative thing as they may have done their due diligence in that sourcing. My point I suppose is the product is a rebranded one and the original product has no provenance whatsoever; you're buying what Rutlands bought. They may be superb and stand up over time, they are clearly different clamps to the ones they sold previously. They may even turn out to usurp Bessey's position in that market. Bessey's are not perfect, they take some getting used to in operating the clamp in certain situations but the quality or their pedigree is never under question. I'm not knocking Rutlands, just being realistic in their offerings; they fit a niche and people obviously keep buying from them. Rutlands is effectively a reseller of clamps whereas Bessey is the actual OEM and they are world renowned for their clamps.
All I'm saying is that from experience I've never regretted buying Bessey and whilst expensive, the pain of that is often dissipated with long term ownership.