Personally, I would go with English Extension 2... At least for that it is self-directed learning.
I did History Extension as I love history though I found it rather boring and time consuming. The major work is your Historical Investigation, which is essentially a personal investigation into an area or topic of interest... This is worth about 80% of your assessment mark.
This is very long and time consuming and it is often difficult to do extremely well unless you are really good at history. Similarly, you still have to do Half Yearlies, Trials and a HSC exam. In contrast, English Extension 2, whilst requiring a similar amount of work only has the 1 major work and a Viva voce, so as long as you spend your time perfecting it over the year then you won't have that subject to worry about during HSC time.
The kind of research that you do will depend on your chosen topic, but expect to read books and journal articles written by academics (things you probably wouldn't do much in modern/ancient).
As for whether History Ext. is better than EE2, that depends on your own abilities/interests and what you mean by "better". Although there are no exams for EE2, it's known to be quite unpredictable in terms of external marking e.g. someone may get great marks for their major work at school but the external markers might not like it.
History Extension has A LOT of content you are expected to know. As with English Extension 2 it requires a lot of discussion but the main difference is that in EE2, your whole course is moulded around your 1 submit. While in History Extension, while you do have a very important internal project (80% of your mark), you still need to know how to execute essays since both your HSC and Trials will have these essays.
If your more suited to reading a lot of fiction, and are a bit more on the creative side, then you should do EE2.
If you are able to do a lot of quality research, as well as having the dedication to do all the coursework and learning the essay technique, then you should do History Extension
In the end, it comes down to your preference. I recommend you look at both the EE2 and the History Extension syllabi as well as asking the teachers for those subjects for advice before you make a final decision