A Real Money Portfolio means that The Motley Fool will be investing its own money in the listed recommendations. The amount that The Motley Fool is investing and the timeframe in which it will be invested is determined by the portfolio service.
A Model Portfolio means that The Motley Fool has not invested its own money in the recommendations, however, allocation guidance is provided to members including examples of how to balance your money across the investment recommendations.
Neither portfolio type is "better" than the other, they are just managed and approached differently.