This is a very intelligent question. Normally the distinction between verse and prose has to do with the nature of what happens in that particular scene and the kind of characters involved. On the whole, it is the main, noble characters that speak in verse and the more working class characters that speak in prose. However, the main characters will speak in prose if they are involved in a particularly comic scene. Speaking in verse normally gives a character a sense of nobility that those characters who only speak in prose never attain. When we think of these two scenes we can perhaps relate the distinction between prose and verse to the two charcters who are being tricked and their reception of the news.
Benedick speaks in prose because his response to the news that Beatrice is in love with him is rather selfish. He wonders what others will think of him, then feels the need to justify his pursuit of Beatrice in a hilarious manner, making prose a suitable method for conveying his speech. Beatrice however, seems to accept the state of affairs much more readily and does not worry about herself and what others might think of her, determining to change her character under Benedick's love. As such, she comes out of the gulling scene much more maturely, and the verse bestows upon her a kind of dignity that Benedick never attains.