The messages and texts that I have seen tell me that the OM seems to be a very immature man about her age and she seems to be going back in time....very juvenile things from the both of them. They seem to think that they are in love.
If it makes you feel any better (and I know it probably doesn't), this is very typical. Most couples in affairs -- even in their 40s and 50s -- sound like high school stuff. "I love YOU more." "No, I love YOU more."