Advice on my first Job Decision (Accenture Federal MC vs. Deloitte Federal Advisory)

Hi, I currently have existing offers as a Technology Analyst for Accenture Federal Services and Analytics Consultant for Deloitte Advisory. I have a few weeks to decide and I am completely torn with the decision.

My interests lie in Analytics, but I also want to be client facing. I desire a healthy combination of project management and analytics while building the skills that come with working with a client. I chose Federal due to the impact and fulfillment that comes with the public service work. I am passionate about a few government organizations that I would love to work with. Another important aspect of the decision is I have firm plans to attend a top MBA program after 2-3 years of working. I want to choose the company that would set me up to be the most enticing candidate for these programs.

The money is basically the same. I would be paid well at both, and this is less of a factor in my decision. The offices are both in DC and relatively in the same area. I also think I would find my place in both cultures and I met great people at both organizations.

My thoughts on the two:

Deloitte
I believe Deloitte has more prestige and brand recognition than Accenture. It also seems they have better skill and leadership development; they have a whole facility for development, Deloitte U. Everyone seemed very ambitious, smart, and continuous learning was emphasized at the events.

The position seems more limiting. I have heard projects are assigned to you and there is less flexibility. I also know Advisory doesn't hold the same prestige compared to Consulting; although, I do not know the difference and have yet to receive an answer in how the projects would differ from Deloitte Advisory-Analytics and Deloitte Consulting Analytics.

Accenture
I think I would like the position much better. I have heard people are encouraged to find their own projects and develop the skills they choose to. I also would be in Consulting, which again I think I would prefer over Advisory.

I am not completely sure of my future plans after my MBA ambitions. I have interest in Tech Strategy. I also could see myself continuing down the Analytics path and choosing to work for a smaller company or FinTech. Leadership development is important and I would really like to move up to a significant management role in the future.

I am in need of non-bias and honest advice. It has been difficult to find the right advice from people who have a perspective of what it may be like at both companies given my interests, as well as how these companies and the positions come across to MBA admissions.

Additional Questions:
1) Is Deloitte Advisory still more prestigious than Accenture Technology Consulting in MBA programs perspective?
2) A good explanation of the differences in the type of work between Deloitte Advisory and Deloitte Consulting
3) Which position and company would be the best launching pad for my future interests?
4) How do the two companies compare?

Any help/advice/guidance is immensely appreciated. THANKS A TON!