Brands of GPU does not really matter most IF they are using the ref cooler.
But if talking about branding, each brands have their own way of cooling the card down. On top of that each brands have their own unique gpus with Bios and their own PCB design to do their own overclocked speed out of the box.
Lets start with other "non" popular brands
Palit - Nvidia Vendors, Cooler code name: Jetstream, Special card cooler code name : Super Jetstream
Powercolor - AMD Vendors, Cooler code name: PCS+, Special card cooler code name: PCS+ Turbo Duo
Zotac - Nvidia Vendors, Cooler code name: AMP!, Special cooler code name: none so far iirc.
Sapphire - AMD Vendors, Cooler code name: Dual X or TriX, Special cooler code name: none that i can recall but cards like Toxic uses TriX cooler.
Major brands that carry both Nvidia and AMD such as:
MSI - Cooler code name: Twin Frozr, Special cooler code name: Tri Frozr specially used for Lightning Cards like the r9 290x.
Gigabyte - Cooler code name: 2x Windforce and 3x Windforce. No special cooler yet for their Gigabyte Ghz edition 780.
Asus - Cooler code name: DCUII. Special cooler code name: Still DCUII but with slightly better implementation with ROG cards such as Striker, Poseidon etc.
All of the brands will have the same thing in mind, is to cool the card down to its very best. The only card that post great challenge in cooling down is the r9 290(x).
They went through 2 types of cooler in order to cool it down. And so far the best i have seen is the r9 290x lightning featuring its Tri Frozr cooler that can widthstand 500w TDP worth of Heat Output. A rated 94deg card that cools to a mere 7X range yet sustain a very high oc out of the box.