Mutual Funds and Stocks provide attractive investment options to different people with different risk appetites and time on hand. Funds charge you for professional services, yet far more Indians prefer to hold stocks individually over trusting a fund. Here are some factors to consider for you to figure out what might work best for you-

1. Risk Appetite: In theory, the biggest difference between Stocks and Mutual Funds as investment instruments is the Risk-Return Ratio.
Traditionally, this has meant that if you’re willing to take the risk of your investment actually going to loss and you having less money than what you started off with, in the hopes of higher maximum possible returns, you should invest in Stocks, or in Mutual funds otherwise. But it should be noted that “risk” may have bigger implications here. Buying the stock of a particular company makes you vulnerable in a sense greater than just the company not turning a profit that quarter. Your investment now is instead dependent on a number of factors.
If you do take the risk and are unable to recover the initial amount, you have essentially lost all your investment, whereas this would have been balanced out by other well performing companies/securities in the case of a fund. The reasons for not turning these expected results can vary from straightforward lack of good organization to just sheer luck.

2. Research: Investing in the stock market is fundamentally choosing a company you believe would be able to sustain its profits and/or grow in the future. To be able to make informed and confident decisions, ample and effective research is necessary. This research includes making scientific conclusions on how the company has been performing, how the sector the company is in has been doing and is projected to do, what strategies has the company adopted to further its profits etc. In order to do that, you should be able to read (and read between the lines of) financial reports, appraisal of how the economy is doing, and effect of various factors like government policies and company management on the performance of the company. There is only so much information you can should be able to gather.
On the flip side, while Mutual Funds save you all the hassle and let a team of experts do that for you, you still need to be updated about various funds and be able to judge one from the other. Historical performance is one indicator among many for you to make a choice. For example, past performance would tell you how the fund has been doing, but drawing any conclusions from this information requires both inside knowledge like if the fund manager is still the same and macro-level knowledge of how the economy has been doing.

3. Long term regular involvement with investment: Stocks tend to be more volatile and responsive to market fluctuations than Mutual Funds that invest in an assortment of stocks and bonds over different sectors. This is because a fund manager is already responsible to respond to the market changes by adjusting your investment to reflect your/the fund’s risk appetite. 
When you invest yourself, you are the only one responsible for that, which is to say, while investing in the riskier option, you also have to be responsive to your research and shift your investment from one stock to another accordingly. Not only do you need to have researched all your options, but this also requires you to check in regularly with your investment to judge if any tweaks are required. This process is completely forgone with funds.

4. Diversification
: A well-diversified portfolio would have simultaneous investments 25-30 options. While investing individually, achieving this diversification requires a sizable corpus to begin with.
On the other hand, buying units of a fund that has further diversified optimally, allows you to achieve the same benefits of diversification while not having to fund all of it yourself.

Investing in Stocks is a continuous and ongoing process while Mutual Funds may be seen as a comparatively hassle-free alternative for the common man.