Interesting point parttimer. When we introduced our 'new' automated system, we had to demonstrate to both the operators and relevant CAA's that the manual & automated loadsheets were tha same (give or take the allowance for error on a manual sheet). In all cases we were able to prove same. That said, we are a cargo operator and work on known weights rather than 'average' pax weights.
At the end of the day, most manual sheets are a compomise with restricted envelopes to ensure that any error in calculation will not put the aircraft in an unsafe state. In my time I've seen and used just about every type of manual sheet, drop line, Xmas tree, adjusted weights, whizz wheels etc. and even resorted (in my young & foolish days!) to the 'shiny bit of the nose gear' calculation!
At best, a manual sheet will give you a result that could be up to 10% out while an automated system, if properly set up, will give an accuracy down to 2 or 3 decimal points, assuming correct weights are used. That said, the automated system will still only give an approximate figure is 'standard' weights are used for pax & baggage. The old addage of 'garbage in, garbage out'.
Responsible operators will recognise this and, like the manual sheet, will curtail the envelope to ensure the aircraft is never out of limits.
Based on the above ramblings, comparing a manual to an automated loadsheet will always show some diffence because of 1) the thickness of pen & judgement of the person completing it and 2) the compromises made in the production and printing of the manual sheet.
RT