Do most top brands deal with local branding agencies or international branding agencies?

That will depend most of the time on whether it is an international or a local brand.
International brands might use both depending on what their global strategy is.
International brands might use international agencies when it comes to implementing a global branding activity and a local branding agency when it comes to adapting each branding activity to each market.
Local brands will also use both.
After all it is about how well the brand strategy is reflected and how great the execution is.

It would depend on the cost, quality and service

yes we can consider local procurement depending on the availability some products are very strategic and some are bottle necks that have scarcity in supply

local purchase can improve the local market.

of course we should always take chances with all resources we've got

It all depends on their budget. 

Depends on the quality, presentation and service catch up with international branding, local branding is more adventageous.