Both are valid Global Explorer itineraries, and both are just under 34,000 miles (according to gcm.com)
The Global Explorer allows the PPT-AKL flight (using the QF codeshare on the TN flight)
The Global Explorer does not have the rule regarding maximum number of flight segments in a continent; instead it restricts the number of stopovers (to four per continent)

Except for the PPT-AKL flight, both itineraries are also valid 5-continent Oneworld Explorer itineraries. Since a 34,000 Global Explorer uusually costs the same as a 4-continent Oneworld Explorer, you are better of purchasing the Global Explorer.
Perhaps this explanation will make it clearer to you what the 4 flights per continent means:

• taking your visit to South America as the example
• you arrive in the continent flying JNB-GRU and you leave the continent flying IPC-PPT (IPC is in Sth America, PPT is in South West Pacific)
• between those two flights, you are allowed up to four flights within the continent of South America - you have three in your itineraries (GRU-BUE-SCL-IPC)
• you can also have surface segments in the continent if you wish
• you are still restricted to a maximum of 16 segments for the whole itinerary

For further reading, this thread discusses the differences between the two ticket types - http://www.flyertalk.com/forum/onewo...rld-explo.html (BUT note: the list of additional airlines in the first post is way out of date; the post is from 2013)

Other points:

• Egypt is in the Middle East; both ticket types therefore allow you to end your itinerary anywhere in the Middle East
• Both tickets only allow two stopovers in the continent or origin; to comply with this you will have to make either LHR or DOH a transit
• As Calchas has just pointed out, you can ticket with any airline on the itineray; it does not have to be the first. For the Global Explorer that PPT-AKL flight is the issue, but any of the major airlines will have a ticketing agreement with TN (perhaps QF would be the most logical choice for you)