There is a lot of differences between cash and tournaments, but the most important ones for professionals especially is the nature of each of the games with respect to bankroll/finances.
cash games have lower variance. The results of cash games sessions have a more direct association with your skill, meaning that when you play well you will tend to win more often. In cash games, you can also rebuy whenever you choose, you are not out without any winnings if you run out of chips because of a suckout. The results of cash games are also realized instantly, if you play really well and run average, you will probably win money during that session and you can stand up whenever you like.
Tournaments have higher variance. You will need to have a larger bankroll and may go days, months, potentially years without a notable cash. This is a bit harder professionally, as you may not get any of your bankroll (that you are living off of) back for a long time. In tournaments, you can be the best player in the tournament and still have mediocre results in that tournament because of run-bad or suckouts. Another thing to note about tournaments is the large difference between a 1st place cash and a 2nd place cash. Often times this can be thousands of dollars, and one heads up match with 30bb each does not always guarantee the better player wins. After a specified amount of time, you will not be able to rebuy either, so if you lose you are out and done playing.
If you plan on playing live, keep in mind that tournaments may often require travel to find the tournaments with the best structures. Recreational players may also find that the time commitment for multi-day tournaments is an obstacle, depending on the tournament and whether or not they have other life commitments.
Cash games have a lot more flexibility and it is mentally easier to maintain a bankroll, but you lose the possibility of large scores.
Consider which you are best at, what your schedule will allow, and how many buy ins you have in your bank roll. Also keep in mind that it is not a bad thing to play both. You can play cash games the majority of the time and mix in some tournaments when you feel comfortable with the structure. Studying both will not make you bad at one and good at the other.