The Visitor Event Guide/Discussion.

Logic and my observations so far make me inclined to believe number of upgrades are whats important.

Yup. It's the Upgrade Slots that counts. I've noticed increase of damage done and reduction in damage received on a character with Visitor armor using just Connection Cells (Speed, Jump, Accuracy, Avoid).

By the way, in case some of you guys missed it:

On level 35 Gunslinger:

Helmet: +1 Roora Core, +1 Speed Connection Cell = Powerful Visitor Helmet.
Overall: +1 Hase Core, +1 Speed Connection Cell = Dexterous Visitor Overall.
Gloves: +1 Hase Core
Shoes: +1 Hase Core, +1 Speed Connection Cell = Dexterous Visitor Shoes.

Getting the first bonus from Visitor Set (+20 Defenses).

Testing done on Level 33 Page. The Cells description is missing stats:
+ 1 HP
+ 2 Weapon Defense
+ 2 Magic Defense
+ 1 Avoid/Accuracy/Speed/Jump

Avoid Cell transforms into Power Visitor gear.
Accuracy Cell transforms into Lucky Visitor gear.