The morgan horse is generally better for a beginner because it is known for its gentle temperament. The Morgan will be easier to train and manage compared to other breeds. Additionally, Morgans are versatile horses that can be ridden in many different disciplines.
However, the Quarter horse may also make a good choice especially if you are interested in trail riding or show jumping. Quarter horses are also known for their gentle dispositions.
Neither Morgan nor Quarter horses require extensive training to begin riding which makes them good choices for beginners who do not have much experience. Either breed can be a great all-around horse for riders of all levels.