A trading edge is an advantage over other market participants. Its difficult to find, its duration is usually for a limited period of time because markets change all the time (days, weeks, months, and infrequently years). Most investors don't even know that edges exist.
In order to succeed with trading, not only must one have a trading edge but it must be combined with good risk management. Otherwise, one is likely to join the majority of traders who lose money.
You've asked about the pros and cons of trading in two different scenarios. As an indirect answer, I'd offer that it doesn't matter what they are unless you have an edge in that market and you practice disciplined risk management. What works in one of those markets isn't likely to work in the other. High volatility or low volatility shouldn't be criteria for deciding what and where to trade. Your skills should.