How to make valuation apples to apples with a participating preferred structure

Hey, I was wondering if someone could help me figure out the math behind participating preferred vs. vanilla structures

Structures like participating preferreds have advantageous return profile properties versus a regular preferred investment given it allows the investor to double dip on proceeds. Therefore, the enterprise value of the two offers (one being a participating preferred and the other being non-participating) are not comparable. The participating preferred structure allows the investor to offer a higher enterprise value, but it may not necessarily be the better offer to the seller due to the properties of the security. In other words, the EVs are obviously not "apples to apples". 

This much makes sense to me. The question I have is, how do we compare the EVs on an "apples to apples" basis? Just curious if anyone here knows the math or conceptually how to think about this.

Let's say there are two investment offers, both $200M and one is a regular pref and one is a participating pref. The non-participating pref values the company at $1.1bn. The regular pref values the company at $1.0bn. How do we figure out which is the better offer if we are the seller? In other words, how do we figure what the $1.1bn participating pref value is equal to in a normal structure? Is it equal to $0.9bn, $1.0bn, $1.05bn, etc. 

Was talking to people about comparing these structures and intuitively and directionally know that the participating pref allows a buyer to offer a higher EV, but I just don't know the math to figure out how to actually compare it. Maybe some people in PE or IB know.