I don't think that one style is better than the other, just different. When done well, both styles are beautiful to watch.
The reason for the different styles is related to different histories on both sides of the ocean (IS in England and AS in the USA). While both styles are danced both competitively and socially, IS evolved as a competitive style first with social dance being of secondary importance. IS has been codified and standardized for use worldwide by the ISTD and IDTA into the Standard and Latin Syllabi.
AS evolved as a social style first with competitive dance having secondary importance. It was developed mainly through Arthur Murray (AM) and Fred Astaire (FADS) franchises. Apparently, Arthur Murray believed that IS was too difficult to master, so developed his own methods and syllabus for social dance. Within AS there is no one syllabus. AM, FADS, and several others have published their own syllabus. Due to copyright protection, independent studios are not allowed to use an AM or FADS syllabus. While this isn't a big problem for social dancing, it causes problems in competitions.
What are the differences?
Standard/Smooth
International Standard includes five dances, waltz, slow foxtrot, Viennese Waltz, tango and quickstep. American Smooth does not include quickstep. IS technique is used as the technical basis for AS Smooth. At the highest level, the only other major difference is that AS allows the use of open positions and spins (i.e. things like underarm turns in waltz are allowed in AS).
At the 'Bronze' level, American foxtrot differs from International foxtrot by allowing the use of SSQQ timing. AS silver and up use the same SQQ timing as IS. AS foxtrot is easier to learn as a beginner and is more flexible for social dance situations. IS foxtrot is acknowledged as one of the most difficult dances to master.
The technique allowed in AS smooth is more flexible for social dancing and can be adjusted to suit a particular situation. This makes the style very well suited to social situations where the dance floor may be very small and/or very crowded.
I think that it is interesting to note that IS Standard couples essentially dance AS smooth in their show routines (i.e. open work).
Latin/Rhythm
The differnces between IS Latin and AS Rhythm (the term used to describe AS latin) are more apparent. The five IS latin dances include: cha-cha, rumba, samba, paso doble, and jive. The five AS rhythm dances are: cha-cha, rumba, bolero, e.c. swing and mambo. Other dances like samba, west coast swing, merengue etc. are often danced as single dance events in AS competitions. The AS rhythm dances (except for swing) are based on Cuban rhythms.
IS rumba and AS rumba are completely different dances. IS rumba timing is QQS with the first Q on the two-count. AS uses SQQ timing stepping on the 1-count. AS rumba is also danced to faster music (32 mpm). Bolero is danced to slower to slower tempos (25 mpm).
The other major technical difference is with cuban motion. This difference is usually described simply that in IS you step on a straight leg while in AS you step on a bent leg. However, this description is simplistic. The body actions in either style occur from the bending and staightening of of legs and from actions in the back, chest and abs. The difference occurs in the timing of the straightening action.
AS swing music is slower at 36 mpm. However, IS jive and AS swing are (if you ignore music tempo) essentially the same dance at the most basic level. Only at higher levels (silver +) do differences show up that change the 'feel' of the dances.
I hope this helps you to understand the differences. Many discussions on this subject turn into a "my dance is better than yours." I don't think its a case of one being better than the other, just different.
Regards,
Blair