With equities, you need to have a directional bias With options, you need to have a strategy or directional bias. You can set up you trade to profit from a move or lack of a move. You can also do more complicated strategies that require more understanding of options. The answer to which is safer or more profitable is not a simple answer. Whichever one you can find an edge in will work best.
You have better risk control with options. If you're bullish on a stock that's at $100 and you buy the stock and it gaps lower overnight to $70 you lose $30 with no opportunity to get out in between. If you bought an ATM call for $1 you only lose $1 on the overnight gap down, but had the same upside potential (less the $1 cost) Owning stock is riskier.
Options are a good idea if you can identify common mispricing assumptions. e.g. the standard options pricing model assumes that volatility increases with the square root of time. this is false in certain circumstances.
Very difficult for an option market maker with an automated trading system let alone a retail manual trader.
This is a common misunderstanding. Of course future volatility is calendar-dependent -- earnings, FDA decisions, Fed meetings, economic reports, etc -- but everyone knows this, so there are no "mispricing." Marketmakers don't naïvely believe B/S prices, or root-of-time. They aren't dumb.
Options are far way more profitable than stocks ... -- if you know what you're doing. ...but also, with that better profit, comes generally equally bad risk. With options you can make %-wise in a day...what stock investors make in a year. You're asking a very basic question, you should do a little research on the topic yourself before posting such a question here.