It's a large subject with many niches and complexities, but some of the main issues are:

Use of batteries in vehicles: Battery storage versus hydrogen storage for a fuel-cell car. A fuel cell car uses the same electric engine, but hydrogen, being the smallest molecule, seaps through most tanks.
Recovery of energy through dynamic breaking. This is one of the most useful properties of electric vehicles, and is usually not a capability of fuel-cell cars unless there is battery storage. Not usually mentioned is that batteries don't typically charge at a very fast rate, so energy storage capacitors are used, which can be charged almost infinitely. They cannot store as much energy as batteries, so they are an additional complication to electric cars. I heard several years ago that lithium ion batteries can be made that are capable of being charged almost as fast as capacitors, so maybe they'll simplify the problem. The main issue is that you can't store near the same amount of energy in even the most efficient battery as you can store in a fuel tank with gasoline. And the physics apparently says that you never really will. Lithium ion allows relatively light batteries with good cold storage characteriestics, and they are getting better. Also, i think lithium is relatively plentiful and innocuous, but I'm not up on the reality of how long they last and how hard they are to recycle. There are real expense and recycle issues with the nickel in the Toyota Prius batteries. Toyota will buy back the battery after some number of miles. Lithium ion have that burst into flames issue but this has been 'solved' (so far) by providing the battery with its own governing circuit which monitors it for heat feedback issues and gives it a certain lifetime after which the battery must be changed out. I've been told that when laptop batteries go dead it is sometimes becauyse their self-monitoring systems have simply gone 'time's up' onT them.

Meanwhile, for stationary power systems, weight is no limit, just safety, reliability, lifetime cost. A few minutes of high power might not seem like much, but they count for a lot in the electric power world because they assist power plants with sudden high demand. For instance, every time you start up a regular large electric motor, it draws from six to twelve times its running current for up to a minute to get up to its operating speed. Another thing that can happen is when you turn off a major generator while turning on another. This may take a few minutes. Often for reliable power, you have both generators running sharing the load all the time, which allows reliability but burns a lot of fuel. The power people have several terms: Rolling reserves, standby power, base load. What it all adds up to is that the newer renewables, wind and solar, are not as reliable because of stuff like weather and cloud cover. Of course, the most reliable generators are renewable too, big dams and hydro, but they go along with big-time environmental changes.
Big battery banks are heavy and expensive, but reliable.
Other forms of transitional power supply are spinning weights and compressed air. A reliable but environment changes is to pump water uphill, store it in a reservoir, then generate it hydro-style when you need it. It works well until it doesn't.

So battery storage is a part of the future, and certainly can be a part of the hype given the way people tend to overshoot the science to sell an idea.

Amory Lovins of the Rocky Mountain Institute, used to remind us that an unnecessary watt saved was just as 'good' as an additional watt generated. He called this 'Negawatts'.