A consultant works more with people and less with software, though you need strong technical skills to be any good at it. A developer (engineer) spends most of their time doing problem-solving while a consultant spends most of their time communicating. Both roles involve analysis.
Following the engineer path probably offers slightly better job security (it’s very easy to hire and fire consultants since they tend to work on projects for relatively short periods). However, the consultant path probably offers more flexibility, as you get experience of a lot of different workplaces. It would also usually involve far more travel and time away from home.
Right out of college, there will be far fewer options for consultancy as most consulting companies will want more proof that you’re good enough technically. Improving your skills as a software developer in no way reduces your options to become a consultant at a later stage when you’re on a higher level technically. It’s easier to go from being a software engineer to being a consultant than the other way round – first get the knowledge, then share it. If you’ve been a consultant for a few years and ended up not doing so much programming, that might make it harder to get a programming job (on the other hand, you might be lucky and find an employer who would value your wider experience).
Senior consultants are paid WAY more than senior software engineers in most of the industry – the exception being some of the huge software companies that really value having some top class senior engineers. However, at the junior levels and certainly straight out of college, there’s no real difference. Either way, you’re there to learn and add a small part to a team effort.