internal - i have the K-Wing compacts. it's not like "totally internal" - there is a groove on the underside of the shoulders of the bars that leads to a channel on the underside of the top of the bars. no problem routing two cables through them. i didn't think they were flexy until i got on them on a trainer, and now they seem very flexy. i got them after it got cold out, so i don't have a frame of reference for real road riding yet.
unbranded chinese - i got these and tried them. felt plenty stiff, no clear problems. ended up selling them to another forum member because i didn't like the bend. he posted many times that he liked them. for $30 or $50, you should try em.
integrated = grooves. on my last build, i did a layer of electrical tape along the whole bar instead of just one or two spots. made the cables feel very stable.