I love how this thread morphed from "Which wonders should I build and when" to "Are the Hanging Gardens better than the Temple of Artemis". This is prince, there should not be a choice. It'll take the first 80 turns (on epic) to build basic infrastructure in the OP's 6-9 cities and the Great Library rush to national college, then they can build or conquer both whenever they want. The real choice is whether they want to open Tradition first to get faster border growth and 3 culture per turn before messing with liberty, and then it takes 4 total policies to get to Collective rule and speedy settlers instead of 3, and that delays things a little. If OP does that, he can build them both easily after NC, although I think pyramids are more important for a wide empire since tile improvements are a higher priority than wonders. If not, he gets to waste a policy opening tradition just to build the Hanging Gardens, which is unacceptable.
I've always thought Hanging Gardens was better for a tall empire with 3-5 cities as opposed to TOA being better for Wider empires with 6-9 cities? Free garden plus 6 food is great for 1 city with no happiness constraints, and 10% growth in all cities plus cheaper archers is perfect for major happiness problems caused by settling too many cities too quickly. Cheaper comp bows and cross bows are also good for dealing with cranky neighbors who are mad that you built 9 cities in your corner of the empire.
Also, TOA's placement in the tech tree is ridiculous, being right there at the bottom beckoning to be built before basic infrastructure as a giant n00b trap! I hate early wonders for this reason alone, the AI always gets them first above king/emperor, and if you are dumb enough to try and build them yourself Shaka's impi's will be knocking on your front door while you have nothing to defend with but a warrior, scout, and 400 gold from 30 turns of lost great library money (I exaggerated here, sorry in advance)...