I guess it really depends on the artists who portray the primarchs in their armor. I'm 99% sure the primarchs are wearing power/terminator/artificer armor. In the Forgeworld Horus Heresy Book, each primarch has a named suit of armor. For Horus, it's called "The Serpent's Scales" and is described as "Horus' unique suit of terminator armor". Fulgrim's "The Gilded Panoply" is described as artificer armor and Mortarion's "The Baraban Plate" is a "of his own design, fusing power armor technology with his own lore". Keep in mind that they all have 2+ saves. The only primarch so far which doesn't have power is Angron, who has the "Armor of Mars" which is described as being "modified from his gladiatorial armor in which he fought as a slave". Sadly, Angron only has a 3+.
As for the backpacks, none of the forgeworld primarch models have backpacks. I suppose that the primarchs would have access to the best technology the Imperium had to offer at the time. Horus' terminator armor was described as having been designed and continuously improved by Kelbore Hal, the Fabricator General of Mars at the time. I'm sure they could design power armor without the need for a backpack power source. I'll go out on a limb and say the Forgeworld books and models are official depictions of the primarchs since they are directly put out by GW. The HH book series depictions can be very inconsistent since there are a lot of artists who design covers.