Does a competitve or integrative model best describe retail strategies for online & instore promos?

A big question, and the answer is "It depends". There are still a lot of retail merchants who view the web as cannibalizing their store sales - but that's because compensation strategies are channel specific. The more clever retailers are associating web sales with their closest stores, because that way the stores are incented to a) encourage customers to buy a product on-line if they don't have it in the store and b) fill orders that come from the on-line channel.

In terms of promotions, the impact of the smart phone makes channel-specific promotions very difficult to execute. The bottom line is the customer will buy from the channel with the lowest price. The reason why we've started using the term "omni-channel" is because all selling channels really do have to be in synch. There is zero value in making them competitive. It creates mistrust rather than loyalty among consumers.

Retailers' biggest challenge these days is creating a consistent and compelling customer experience across channels. To do that, they need to be as integrated as the can manage - even though their technology and organizational infrastructures may not support that easily.

So in the end, the answer is "integrative".