Can anybody tell me whether it is a better idea to grow tomatoes outside in a growbag or, can the crop be just as good, if you grow directly into the ground.
Better in the ground, I think, given half-decent soil of some depth. The soil doesn't have to be rich. Toms are pretty forgiving of most soils providing the pH isn't too far out of kilter. They like things slightly acid but will cope a degree or so either way. The bottom line, though, is position. They need as much as they can get - 6 to 8 hours a day minimum to achieve full potential.
Plants in the ground also need a lot less water. Watering infrequently - maybe once a week - but very deeply will drive the roots down deep into the soil and away from the surface where they're more affected by surface temperatures. Frequent, shallow watering only keeps the roots shallow.
Plants in the ground also need less fertiliser. Providing the soil is half-decent, one feed a couple of weeks after planting out, another one when the first fruit is setting, and one later in the season will be sufficient. They won't suffer. Toms are the sturdiest of critters that respond best to tough love.