A little history...
Where do we stand today?
Many developers started to phase out the use of Flash for slideshows over the last few years for a number of reasons - though the main one for me was the lack of compatibility with Screen Reader software and therefore the potential problems that using Flash could cause in terms of the Disability Discrimination Act (DDA) and an awareness that not all home users were confident enough to install the Flash player - many users being wary of installing add-ons to their browsers due to fear of hacking and malicious software.
Today we favour the JQuery approach as it allows us to quickly create attractive slideshows and be sure that they will work on all devices and all browsers. Working with JQuery also means that we can combine effects, for example adding a hover maginfier to a slideshow on a brochure websites.