Different, yes. Better, no.
In another thread, I wrote recently about my dc's marvelous experiences at an arts high school. They are enjoying a creative, supportive learning environment at a school that has been ranked #1 in our city for academics. I don't particularly care about the ranking (and I don't actually think it's accurate), but there's no doubt that they are getting a solid education in core subjects while attending a school that provides daily arts instruction.
As I wrote elsethread, there is simply no other environment (and particularly, no homeschooling environment) that could replicate this experience for them. Every day, they are immersed in an arts education of the highest quality and they participate with other enthusiastic, motivated, incredibly talented students. For years, they've taken private music lessons, played in ensembles, signed up for drama groups and art classes and all sorts of extra-curricular activities that happen on a once or twice a week basis. While those activities were valuable, they just can't compare to a consistent, daily exposure to an arts experience with a wide variety of students who have different interests and specializations and knowledgeable, skilled instructors.
For most of their elementary years they attended gifted programs, where divergent thinking, critical thinking skills, and experiential learning were encouraged. They were exposed to many different methods of instruction and information gathering. Learning is one thing, but effective communication is another. The ability to communicate is critically important and many people flounder or fail because of poor skills. My dc's teachers have excelled in nurturing communication skills in many different media. My dc have prepared oral presentations, video documentaries, photo essays, poster presentations, essay and narrative writings, science reports, business and marketing plans, and blogs. They may have done some or all of these things while homeschooling, but I don't think these communication skills would have had a similar priority. I doubt that they would have been developed to the same degree and with the same facility and natural integration into an educational program. After all, if you only have a couple of people in the home to communicate with, there isn't a pressing need for a skillfully produced presentation on a subject, and even less opportunity to observe and learn from others' attempts.
Whatever school setting they have attended, they have been part of a diverse multicultural community. They have learned on a deeply personal level to integrate happily with people from different cultures and to respect and appreciate other heritages. They are mindful of different beliefs about food, dress, and traditions. After years of co-existing on a daily basis, they don't even notice the natural adjustments they make to accommodate each other. It's a little like the difference between being a tourist as opposed to actually living in another country.
It's possible that some attitudes and behaviours are easier to develop if a child is in an independent learning situation outside of typical schools. I'm thinking of divergent thinking, internal motivation, and experiential learning born from curiosity and experimentation. The oft-heard criticism against schools is that they don't do a good job of encouraging these things, thanks to standardized testing, grade obsession and rigid curricula. I don't think it's impossible or even difficult for a schooled student to develop these traits and I don't think they are well-developed in every home learner either. My dc enjoy learning with other students. They are motivated and inspired by their classmates. Since much of their schooling has been project-based, they've learned immense amounts of fascinating material from their classmates' projects and presentations. At the same time, they've developed leadership skills, communication skills, and project management skills, and aren't lacking in divergent thinking, internal motivation or experiential learning.