1. Both plants draw similar nutrients from the soil at the same times. So in essence they are in competition for resources.
2. There are claims that Basil somehow enhances the flavor of the tomatoes, making them sweeter. Personally I have never been able to tell the difference as I have planted tomatoes and basil together on numerous occasions in the past with lackluster results. But some people swear by it, so perhaps it's a placebo effect ?
3. Basil tends to be low growing as opposed to tomato plants, it also requires lots of sunshine. Basil is shaded by the tomatoes and, being shaded by the larger tomato is sometimes deprived of the much needed sunlight to bask in. In the midsummer heat the Basil will benefit from a dose of late day shade provided by towering tomato plants, but certainly not 24/7.
4. Basil is said to repel insects. I wish someone would tell that to the white flies that infested my basil a few years back. If you want scientific validity for the 'Basil repels Insects" claim, good luck trying to find it, let us know how you make out. Although some gardeners claim that planting basil near tomatoes seems to help in keeping bugs away, there are others who state it makes no difference whatsoever. And then there are gardeners who through their own experience believe that basil harbors some of the very same insects it's supposed to be deterring.