Offers & Start Dates

I am an MBA in Finance with 6 years of client service, operations, fund administrative, compliance, etc skills/experience. I am currently working for a well known investment bank but looking to move out of the day to day operational type environment. I have been offered (and accepted) a Project Management position (no financial service/product knowledge will be used in this role) with a well known financial firm.

We have been thru the back and forth of negotiating salary as well as a start date. I was able to confirm a start date a month after accepting the offer. I feel this whole process was not smooth as usual so I think I may have already put a bad taste in their mouths.

However, I have also been in a long interview process with a second tier consulting firm for a risk management consultant position. I have secured a final interview with Senior Mgrs. The last round has been moved to a date that is past the start date of the job I already accepted. I prefer the consulting route so I was hoping to get the last round of this interview in and (hopefully) secure the job before having to start the PM job, which was just a security blanket.

So my question to the forum is: should I continue with the process of the final interview and if I get it then terminate employment with the first offer suddenly after starting or do I take this as a sign and just go ahead with the first offer and see what the PM world has to offer?