The answer to this question is likely to be heavily influenced by your level of mechanical ability. If you are able to prepare a car to a decent standard, and have sufficient spare time, then running your own car is a valid option. It also helps considerably if you have really good mates or relatives who can help you!
The advantages of going with a team are that you can concentrate on just driving, your time commitment is considerably less and, provided you have chosen a decent team, they should have considerable expertise in preparing and setting up rally cars.
Also, it is worth doing your research before committing to a deal with a team. Most rally teams are honourable and professional, but like any industry, a few may not be so!
It is quite common for competitors to opt for somewhere between these two alternatives: looking after the car themselves for all the day to day stuff, and calling on the expertise of a team or highly competent mechanic, or specialist body shop, when things get tricky.