How much difference there is between a BSN and a ADN plus BS in another field depends upon the specific schools in question. Anyone who says they are "always the same" or "always different" is giving you an answer too superficial to use in your decision-making.
Some ADN programs include most of the same content found in most BSN programs -- but not all. Also, some BS programs in other fields include the content that is "missing" in a particular ADN program, but most do not. Also, you must consider that each discipline has its own traditions and perspectives upon which it is founded. Taking similar courses grounded in another discipline would be helpful, but might not include some key points pertinent to nursing. It can be very helpful to take classes in another discipline -- but in order to maintain a nursing perspective and remain grounded in the nursing disciplines, those courses need to be taken IN ADDITION TO nursing courses, not INSTEAD OF nursing courses.
The type of content that is often not included in the ADN program, but is often included in BSN programs includes:
1. More emphasis on nursing theory and the major schools of thought within the nursing discipline
2. Nursing reseach -- methods, particular problems, issues, etc. related to NURSING research that might be different from the research traditions of other disciplines.
3. Familiarity with the nursing literature. Granted, a lot of BSN programs do a bad job of this -- but the better programs have the students writing papers, researching topics, doing presentations, etc. that get the students to explore the literature a bit. ADN programs tend to do less of this.
4. Nursing leadership issues -- not just administration/management, but issues related to the profession and to being a leader (any type of leader) within the profession. Neither ADN programs nor courses in other disciplines would routinely cover that content.
5. Some introductory content related to advanced roles and patient education.
Those are just the things I thought of off the top of my head. It's not that ADN programs never include any of the above topics ... they just tend not to emphasize them as much. Courses in other disciplines wouldn't cover them at all. Unless they have made an extra effort to get that content, people whose degrees are in other fields sometimes find themselves "out of step" with their colleagues who have BSN's and graduate degrees in nursing because they never got the advanced content within nursing. Even though they may have higher degrees, their NURSING education stopped at the beginner level. That puts them at a disadvantage -- a disadvantage that can be overcome, but a disadvantage nonetheless.