It's not about weight or efficiency. If operating costs are lower, it will win out eventually. Current electric aircraft can carry 5 passengers and have a range of 250 miles. They cost half as much to operate per hour, because electricity is so much cheaper than fuel. The main reason why they're not popular is because batteries are expensive. As battery costs decrease, we'll see more of the market adopt them.
Will electric aircraft cross oceans? Probably not. But the batteries are already good enough for useful flights. And you have advantages such as VTOL, quieter operation (allowing you to use urban airports at times when other aircraft are banned due to noise restrictions), and less maintenance.
250 miles isn't nearly as much as it sounds - you need to leave plenty of buffer in case something goes wrong so cut some of that off. You also need to get to an airport and then from the other airport to where you are going. Thus most of the time for distances of that range driving is faster.
The cases where I've seen this in use are from island to island (or mainland) - where a boat is much slower and there is no bridge for a car. A useful niche, but not general purpose getting around. There are also a few people who happen to live near (often on) an airport and work near an airport who will fly, but that is also a small niche.
Will electric aircraft cross oceans? Probably not. But the batteries are already good enough for useful flights. And you have advantages such as VTOL, quieter operation (allowing you to use urban airports at times when other aircraft are banned due to noise restrictions), and less maintenance.