I would say that the CJK Decomposition Data (your first link; henceforth CJKDD) is better of the two, for most purposes. Some time ago I used the character decomposition data from Wikimedia Commons, and there were quite a few popular characters with missing decompositions. Now I checked a few of these characters, and all of them had decompositions in CJKDD, so it seems more complete.
The Wikimedia database is better than before, but still lacks decompositions of some characters, such as 齒, 風 and 龠. Moreover, some decompositions are incorrect, e.g. 辰 is shown as a component of 脈. And in general, the Wikimedia database doesn't show components that aren't separate characters. CJKDD, conversely, contains all kinds of components, including the ones that don't have their own Unicode code points.
Wenlin with its Character Description Language (CDL) is another source of decomposition data that you may want to look at. Even CJKDD has inconsistent descriptions of some characters, and Wenlin seems a bit better in this regard. For example, even though 𨊠 is present in the database, it is not shown as a component of 範 (範 is decomposed as
範:d(⺮,38298), which is in turn decomposed as
38298:a(車,㔾). In Wenlin, 範 is correctly decomposed into 𥫗 and 𨊠. Wenlin uses Unicode Private Use Areas for encoding components that aren't separate characters.
On the other hand, Wenlin has its peculiarities and, for example, decomposes 齒 into 𣦊 and 凵. CJKDD splits 齒 into 止 and 𠚕, which seems much more natural. In the result, Wenlin doesn't see 𠚕 as a component of 齒. Similarly, 曲 a sub-sub-component of 曹 in CJKDD and Wikimedia, but not in Wenlin.
Another difference between the databases is that CJKDD decompositions are consistently graphical. For example, 條 is decomposed as
條:a(39752,条), which is in turn decomposed as
39752:wr(亻,㇑). In Wikimedia Commons, 條 is decomposed into 攸 and 木, which has more to do with the historical development of the character and its radical (which happens to be 木), but not with its modern form. Wenlin provides both the graphical decomposition (based on the CDL data), and the list of all the sub-components that may be associated with this character (in this case: 攸亻丨条夂木). Another example: because the CJKDD decompositions are purely graphical, the upper right part of 祭 is shown as 卩. Wenlin, more correctly, shows it as a graphical variant of 又.