Advantage of the triangle inserts (16 IR AG 60 or 16 ER AG 60) is that you can buy them in full (A60 or G60) or half thread form (AG60). Full thread form tools require two inserts to cover all the pitches (A60 is 16-48 tpi, and G60 is 8-14 tpi), and it actually will cut the roots and the crest of the thread, so you get a more accurate thread form. Half thread (or partial profile) covers the full range with one insert. To make matters worse, the internal (16 IR) and external (16 ER) cutting triangle shapes are different. So you aren't using the same insert for both tools.
BTW, the above assumes you are using at least a 1/2" tool with a 3/8" insert (the 3/8" tools with a 1/4" LC insert only support 16-48 tpi).
The "cut off type" tool only does half the thread form, and I think it is less prone to chatter than the triangle, but that is just a guess, since I only have the triangle type.
What type of material are you primarily cutting? Make sure you buy the right coating. Aluminum doesn't cut great with the wrong carbide coating, especially with no coolant.
With the emco cnc, since it is a lower power and no coolant, I would actually tend to pick a HSS insert. Look at Arthur Warner for insert-type HSS tooling if you don't like to grind your own threading tools.
Arthuir Warner HSS Threading Tools