Almost every engineering degree is considered more difficult than a business degree...most people know that. I know the joke at some schools is the business majors are the kids who couldnt cut it in the engineering majors...although the business kids probably have the last laugh in the long run. As an engineer you will never be poor but sure wont become megawealthy.
Getting a job in finance at a top level bank is very dependent on schools...much like coming out of an MBA. They do draw from a larger pool of schools than they do for MBAs, but if you they dont recruit at your schools then it might not be the best idea. I know a lot of us on here are engineers or folks working in computer fields, and many of us have had amazing success with schools. I know I went to a no name undergrad and trust me my engineering major is more obscure than yours its only offered at five colleges, all of which are very small and specialized....I think in a way it helped me since I wasnt another ME or EE.
I would say before you make a rash decision, check to see who recruits at your school for finance jobs...make sure places you want to work actually come. Find out who is getting interviewed and hired, I know some people who were engineer or math majors and got hired at banks because they were good at the quant stuff and the bank would pretty much teach them what they needed them to do just like for business majors. Your best bet may be to get an internship.
One thing to think about is a lot of engineering majors are in demand right now, that probably isnt going to slow down all that much. However, with the current state of the economy, you never know what the hiring will be like for business majors in a few years. If you look at the long term and know you want an MBA two or three years down the road, your engineering degree and an unusual job may actually be a great benefit...they do like diversity.
Kellogg Class of 2010...still active and willing to help. However, I do not do profile reviews, don't offer predictions on chances and am far to busy to review essays, so save the energy of writing me a PM seeking help for these. If I don't respond to a PM that is not one of the previously mentioned trash can destined messages, please don't take it personally I get so many messages I have a hard to responding to most. The more interesting, compelling, or humorous you message the more likely I am to respond.