Myself, I wouldn't prune either of those plants, but would rather give them some form of heavy support, like a stake or a cage and let them just grow as they will.
Let 'em go. Compared to tomatoes, both eggplants and peppers would be considered determinates. Those secondary buds will push out when they're ready later in the summer. Pinching them out would eliminate most of your crop. Better hope for a warm season where you are!
Barbara
My Aubergine are growing well. The Peppers however seem to have slowed down at about 9" and they are getting very bushy. I replaced all of the soil bed in the greenhouse this year with good stuff. I am puzzled - up until a couple of years ago, my Peppers would grow to about 18" at least and produce lots of big fruit from them?
John
I wouldn't worry too much as long as they look healthy. In my experience, most pepper plants have a very long life in the garden and grow continually [if perhaps slower] as they get older, and there is still quite a lot of growing season left, even more so in a greenhouse. For reference, I planted my peppers [outside] at about the same time you originally posted, and mine are all about the same height as yours, around 9 inches or a little less, and are only just now beginning to bloom. I think a lull in growth at or about this time in their life cycle is usual. It's likely they are redirecting energy from plant growth to preparing blooms and fruit set.