The data collection method determines the budget, the timeline and how far you can trust the results. There is no universal answer: it depends on the audience and the task.
CATI (phone survey) fits when you need a fast, nationally representative sample. Our own call center lets us control the quality of every interview and deliver first data within days.
CAWI (online survey) is the most cost-effective option for active internet users and customer bases. CAPI (tablet-based face-to-face interviews) is essential in the regions, for long questionnaires and when respondents need to see a product or packaging.
In practice we often combine methods: this covers different segments while keeping the budget under control.