We don't really eat at chain restaurants, so we don't eat a lot of places that *do* have a kid's menu. Most of these places also won't give a half-portion and charge less for kids. (I've asked.) Those places that do have children's menu are for frankenfoods I wouldn't let dd eat, anyway (hot dogs, for example) so I don't think she's ever even ordered off of a kid's menu. For the most part, we've always let dd just order what she wants off of the adult menu/standard menu and take home the leftovers.
However, if there is something that we'll both enjoy we'll split it... for example a half slab or ribs is great for the 2 of us, but neither could finish them on her own. She's 9 now and for the most part is able to eat a similar amount to what I do. If we're somewhere that we can't take leftovers home (like on vacation), then my dh will usually finish our portions for us. Dd doesn't split anything with dh because he *always* finishes whatever he's eating. For the ribs example, we'll even split a whole 3-ways between dd, my mother, and me if we're all going to order the same thing. That makes money sense, I think.
We eat out once a week, at a nice sit-down restaurant (often ethnic), so our eating-out budget is high, but it's something we really enjoy as entertainment and not just getting sustenance. We'll sometimes spend 2 or 3 hours at a restaurant and eat multiple courses (especially if they have good, live music), so it's worth getting good food for everyone. Then again, we have an only (but my mom lives with us, so we're feeding 3 adults, too. The way my mom eats, it's like having a teenaged boy in the house. lol) If we had 3 or 4 kids, this whole thing probably wouldn't make sense fiscally or logistically and eating out would be a whole different experience.