Firstly, not to be confused between these two. Both are completely different way of investment.
Biggest advantage of fractional investment over REITs is that fractional investing allows investors complete freedom to choose the type of property to invest whereas in REITs, investors have absolutely no say or no choice to opt as it is decided by the company managing the funds. However, dividend income from REITs ensures regular income.
Fractional ownership is a longer-term investment with a set holding duration, which is generally bounded by a time period but after this duration investor can either exchange or can sell his shareholding. While the individuals who invest in publicly listed REITs often have the option to sell their shares at any time.
REITs are regulated by SEBI and is executed by well laid down norms including professional management having core skills whereas fractional ownership is function of persons at helm of affairs.
Also it has taxation incentives whereas fractional ownership follows conventional tax treatment.
In contrast to REITs, fractional ownership provides you wider range of opportunities and choices and also provides you additional benefits of exploring different places and getting the chance to enjoy the luxurious lifestyle.
Basically it's up to you and your investment objectives. These trends of investment are welcome as it's sign towards maturing market conditions with wider choices / strategy to hold assets.