And while, predictably, neither chain is revealing sales figures, the word from the UK combatant is that it is doing best when it comes to winning a share of the locals' purses.
Talk to Kittipong Thansombat, the 36-year-old who manages the Tesco, known affectionately as George to colleagues and customers alike, and he'll tell you that the British market leader is more than holding its own in the high profile tussle. Tesco was first in with a colourful in-store formula which has successfully pioneered the group's much talked about entry into Thailand Â a country which also has stores from arch-Euro rival Ahold.
Its location, with 129,000 sq ft of selling area at the heart of a specialist shopping mall which also targets the locals' passion for eating out (a Japanese eaterie and a McDonald's to mention just two units), is similar to French neighbour Carrefour's.
Tesco is pulling in more than 70,000 shoppers a week through its 49 checkouts.
The unit, the multiple's largest in Thailand and one of its 16 supercentres in the Bangkok area, trades from 6am to midnight and global retail analysts who have toured its aisles agree that it "incorporates the best of traditional Tesco, while reflecting local needs."
This means a vivid food image, meeting the Thais' traditionally strong demand for fresh products.
And it gives a modern theme to Bangkok's famous "wet markets" where consumer purchases of fish, meat and fruit and vegetables are made daily.
Tesco went into Thailand in 1998. By the end of 2002 it will have more than 50 stores in an operation which has spearheaded its spectacular drive into the Far East.
It plans to invest another Â£3m over the next five years.