Which writing style for uncertainties? There are different ways of writing uncertainty.  The siunitx manual says "In some fields, it is common to give the uncertainty in a number in brackets after the main part of the number...  Alternatively, the uncertainty may be given as a separate part following a sign."

Examples:


1.234(5)
1.234 ± 0.005


Which academic fields use which style in their journal articles?  Does it depend on the region?  Is there any agreed upon standard?
Yes, there is an agreed upon standard and it is specified in the Guide to the expression
of uncertainty in measurement (GUM), section 7.2.2, prepared by the Joint Committee for Guides in Metrology (an ISO committee).

Both forms are equally valid, and people use them indifferently. The first form is just more compact and it is particularly useful in tables, abstracts etc.

For an uncommon usage of the first form, see also this answer of mine on Physics SE.