What are the major drawbacks of using an electric lawnmower?
By far the biggest con is charging battery(ies), although that's becoming less of an issue as battery technology gets better. Any issues with not cutting well, not mulching well, etc are largely issues of older mowers.

Consumer Reports actually starts to recommend some electric mowers as of ~last year. You can read more about their recommendations, but they boil it down to a few points:


Electric mowers tend to cost more up front, but tend to cost less to operate and maintain (by ~$20/year according to their estimates). Payback period is on the order of 10 years, though, making it a long-term investment. You'll want to run numbers using the cost of your electricity and gas for an accurate comparison, of course.
You'll probably want a spare battery (unless you go corded, but those options seem more limited), meaning even more cost. At some point, the battery(ies) will need to replaced as well, potentially eliminating any cost savings compared with gas mowers.
At least right now, there aren't any riding-style electric mowers for large yards. If you have more than ~1/2 acre, electric probably isn't for you.


That said, it seems that the good mowers have good (enough) batteries to last long enough to mow a typical 1/4-1/3 acre lawn on a single charge. You could also go corded and eliminate battery worries entirely.