Of course Strikeforce has much more to lose here. If they did this and their current champs lost to the champion of a smaller org it would look horrible for them. Especially when they're trying to make the mainstream audience believe that they have the best stable of fighters in the world (which is ridiculous).
Bellator have nothing to lose. If they win, awesome. If they lose, hey at least they gave it a shot and no one would think any less of them.