Which is better to use, vanilla extract or paste?

For tea, probably extract. For baking, I use vanilla bean paste mostly when vanilla is the primary flavor and extract when it is to support a stronger flavor (just because paste is so expensive). I always use paste for things like custards and whipped cream because the little flecks of vanilla bean look nice as well as the stronger flavor.

Lots of different opinions out there. Here's mine:
Sometimes, use whatever you have to finish that baking project or cup of tea.
By depth of flavor, for baking, paste is wonderful.
Generally, for adding to tea or coffee, I prefer extract (it gives you enough flavor, and the use of paste here is extravagant).
For cost, paste is always expensive but usually worth it.
Extract is usually expensive, especially in grocery store 1 oz or 4 oz bottles and not worth it.
For economy (and it keeps a long time), get a pint bottle in bulk or baking stores, or infuse beans in liquor at home (takes a few weeks to mature, then you can keep adding beans and your choice of spirits; rum or brandy would be good for tea).