Monitor and Accenture Strategy - Tier 3?

With no doubt I would say Accenture Strategy. 

I've been involved in strategy consulting for a while, and I can say that the jump from Accenture Strategy to MBB is fairly common. Accenture Strategy is clearly Tier 2. Monitor, Booz and the rest of Big Fours are a step behind. I can only speak for the European market though, it's the one I know well.

In EMEA in general there is a difference in exit opportunities between MBB and others (and this difference is way smaller than in US) but then difference between second tier shops for exit opportunities is much more dependent on the expertise you will build within the firm and how in demand it is when you decide to leave rather than which firm you come from. Indeed you will see a lot of variability in post-consulting career paths within the same firm at the same level of exit depending on practice/industry of specialization and on specialization topic (e.g. pricing).

The best way to have an idea on what does opportunities are is to look at LinkedIn profile of employees in those regions and see where they landed.

That said, I would choose monitor Deloitte because it is more established in that space.

hope it helps,

andrea

Can only talk about Europe.
There I would clearly prioritize Monitor Deloitte, as brand heritage and therefore quality of partners is really top notch. 
Depending on your starting point, one potential exit opportunity might be an MBA. In this arena (especially with US schools) you will have great opportunities  in terms of school access as well as financially with Monitor. 
Hope that helps. For further questions don't hesitate to reach out.

They are Tier 3. I would say Accenture Strategy is a bit above Monitor Deloitte.