These are mostly equivalent, but import * has some restrictions that import ... = require doesn't.
import * as creates an identifier that is a module object, emphasis on object. According to the ES6 spec, this object is never callable or newable - it only has properties. If you're trying to import a function or class, you should use
import express = require('express');
or (depending on your module loader)
import express from 'express';
Attempting to use import * as express and then invoking express() is always illegal according to the ES6 spec. In some runtime+transpilation environments this might happen to work anyway, but it might break at any point in the future without warning, which will make you sad.