First, note that these are not licenses, they are professional deignations. You can be an analyst or a financial planner without them, but having them shows that you have taken the trouble to get an extra level of professional training.
The CFA designation stands for Chartered Financial Analyst, and it is usually taken by people working as analysts or portfolio managers at investment management firms (companies that professionally manage large amounts of money) or brokerage firms/investment banks (securities brokerage firms which, among other things, advise the investment managers).
Generally, CFA's are working in the part of finance dealing with institutional investments -- either managing pension plan or hedge fund money, or recommending securities to those who do.
I do not know as much about the CFP designation, but my understanding is that it is taken by those who are involved in advising individual investors, typically with smaller investment portfolios than institutions would have.
As an analyst with a CFA designation, whether working for an investment manager or an investment bank, you would deeply analyze individual companies and industries, to look for good stock or bond investments. You are likely to be more of a specialist, and probably will not be familiar with every investment product.
As a portfolio manager with a CFA, you would be responsible for selecting stocks or other securities to go into a portfolio. You would use in depth information from analysts at your own firm, and from analysts at investment banks. Your scope may be broader than that of an analyst, but you will still be something of a specialist.
As a CFP, you are likely to be advising a clientele of individual investors on financial plans. You will have to know about a wide variety of investment products, including stocks, bonds, mutual funds, annuities, etc. You might be working at a brokerage/investment banking firm that deals with individual clients, or you might be wroking in another setting.
Each profession is hard in its own way. As an institutional investment analyst working for a securities brokerage firm, you have to analyse stocks and market your research. This is hard work.
As an analyst working for an investment manager, you are expected to come up with good stock recommendations for internal use. This is hard work, and a lot of responsibility.
As a certified financial planner, you have to accurately determine the financial needs and aspirations of your clients, and, using research materials generated by invetment analysts, including those with CFAs. This is also hard work, and a lot of responsibility.
So the CFA is what you want if you are interested primarily in financial research and analysis, and the CFP is more for you if you want to do investment planning for individuals.
To get the CFA designation, you must take three exams, each one in a separate year. The exams cover finance, accounting, economics, investments, and ethics. They are hard. There is also a work experience requirement. Check this website for more details:
For the CFP, you need to meet certain education and work experience requirements, and take one exam. Details appear here:
Finally, as to whether you should become a financial analyst or a financial planner really depends upon the kind of person you are. If you really like deep analysis, writing, gathering information and giving presentations, the analyst job may have more if that in store for you. If your passion is helping individual people and families, being a financial planner may be more rewarding.