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The degree of unsaturation of fats can be determined with the help of two type of scale namely iodine number and bromine number.

Generally, iodine number is more preferred over bromine number (Is this statement true? Is it because the Wikipedia article of iodine number is more elaborated than that of bromine number?)

Iodine number is typically found out by using iodine monochloride, $\ce{ICl}$ where the iodine atom gets bonded with the carbon atom having double bond. The more iodine used up to break the $\ce{C=C}$ bonds, higher is the iodine number.

$$\ce{-CH=CH - + ICl -> -(I)CH-(Cl)CH - }$$

But in the 4th paragraph of the 1st page of this link, it is written that:

Iodination is an endothermic process, resulting in vicinal diiodides that tend to revert to alkenes. Consequently, the most common applications of alkene halogenation are chlorination and bromination.

So, in this context, bromination is better and thus bromine number is better than iodine number. The statement contradicts the previous statement i.e. using iodide number.

H.P.Kaufmann method of finding iodine number uses bromine. Is this a better method than using $\ce{ICl}$ considering the disadvantage of iodination?

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Bromine number (and Bromine Index) are based on theoretically good chemistry; however, that is where their virtues end. If these tests are run according to the current ASTM procedures, you are virtually guaranteed to get an incomplete reaction and low (perhaps as much as 50%) results. When properly applied, off the shelf equipment can result in exceptionally good accuracy and precision, but it does require a deviation from ASTM-accepted technology.

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Which is better for measuring unsaturation, Iodine number or Bromine number? The answer depends on how you define "better". However I can tell you which is commercially useful. If we're dealing with fatty acids or vegetable oils, the industry standard test is Iodine number. For petroleum products, the standard test is Bromine number (or bromine index, slightly different). For the two tests, Reference Bailey's Industrial Oil and Fat Products, sixth ed. vol. 1 pg. 172, and ASTM D-1159.

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    $\begingroup$ Could you add some information to support a conclusion and answer the question? While your post is useful, it is more appropriate as a comment or two than an answer. $\endgroup$ – A.K. Aug 28 '18 at 16:49

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