I've split my life between North America and Asia. People ask me whether I prefer business etiquette from one part of the world over another.
How I behave for meetings in Asia (using English, Cantonese and Mandarin):
Bow when accepting business cards (only from the neck for about 10 degrees - I don't bow from the hip)
Accept cards with both hands
Study each card for a moment as I receive them
Arrange all cards face-up on the table when seated
Line cards horizontally (never vertically so that I don't accidentally put the card of someone more junior above someone senior)
Use of honorifics (Mr / Ms) unless they first use my given name
Calibrate the loudness of my voice, tone and speaking speed to be slightly deferential if speaking to someone older
Body language deliberately more restrained and controlled
In the context of this post, "Asia" means my experiences in Hong Kong, Singapore, Korea, Taiwan, Mainland China, Malaysia, Thailand, Philippines and others in the region.
For meetings in North America:
No bowing
Accept business cards with one hand
Pocket the cards
Acceptable (and expected) to converse on a first-name basis
Use my normal voice and body language
Which is best?
Neither.
The "best way" is whatever gets (and keeps) business for the particular context you're operating in at the moment.