Breakers protect wires. The wire to the sub-panel can only be protected by the breaker in the main panel, and that must be correct for the wire's type and size.
Like Ed Beal says, you don't need a master breaker in a sub-panel. The breaker in the sub-panel wouldn't protect the wire to the sub-panel. It protects the sub-panel itself, which is listed for 200A. It can also be nice if you ever get sick of paying the tenant's electric bill and have the electric company feed a separate meter to that panel - voila, the master breaker is there already!
(I'm saying "master breaker" to avoid saying "main breaker", which might be confused with "breaker in main panel".)
If you are hoping for the sub-panel breaker to trip before the main-panel breaker, that doesn't work. Breaker trip curves are complex and unpredictable.
If the 100A breaker is not listed or labeled to work in the 200A panel, then you cannot use it, end of subject. That's the law.
This is a situation where buying from a proper electrical supply house (and not a big-box home improvement store) will be very helpful. You tell them what you want, they will sell you the right thing in the first place, and stand behind the combo. On price, for the behind-the-counter stuff, I find them more than competitive with big-box. Their customers are, after all, electricians who deal in volume and drive past 3 big-box stores to buy there. (Electrical supplies do tend to wildly overprice the impulse-buy grab-candy at the front of the store, so don't go off those prices.)
Since this is fed from a breaker in your main you can do it with both wiring methods but it would be considered a feeder and the wire size would need to be good for 125% of the breaker or 125A the way I interpret the code. If all the loads are non continuous it could be 100% but with all those spaces there will probably be a few continuous loads so better to be safe for the long run.
Best Answer
The conductors will have to be full size to the 200A breaker. Remember what protects the conductor is the 200A breaker if you reduce the conductor size there must be an additional breaker to protect the the current carrying conductor. NEC does allow for the feeder to be reduced for the final 1/3 distance of a feeder which is probably impractical, but it does allow the subpanel to have 150A buss.