Neither ... for one, neither Asus or Acer actually make a laptop. Pegatron makes laptops for both of them, tho each has other sources.
The vast majority of laptops on the market (94% in 2011) are manufactured by a small handful of Taiwan-based Original Design Manufacturers (ODM), although their production bases are located mostly in mainland China.
Major relationships include:
Quanta sells to (among others) HP, Lenovo, Apple, Acer, Toshiba, Dell, Sony, Fujitsu and NEC
Compal sells to (among others) Acer, Dell, Toshiba, Lenovo and HP/Compaq
Wistron (former manufacturing & design division of Acer) sells to Dell, Acer, Lenovo and HP
Inventec sells to Toshiba, HP, Dell and Lenovo
Pegatron sells to Asus, Toshiba...