I would strongly recommend that you not shy away from reading to both of them at the same time. The camaraderie that is built, as you work through, with both of them, to negotiate what you will do with each book - it is priceless. You could let each kid pick a book (or two or three), and then read both books to both of them, all three of you together, but making it clear which book is whose, so that kid gets to "drive" a bit more with his book, but the other still is there, listening and learning. This will teach them that being together and cooperating and sharing (their books and your time) is more important than just getting through the routine or checking off "reading" on the list of activities.
I have done this with my kids and we often read all together. At first it was each kid (and I have four) picking one or two books, Dr. Seuss kind of stuff, and we would read through them. As they grew older, we graduated to books like Andrew Clements' (author of lots of really good books accessible to younger kids but fun for older kids and adults) and the Chronicles of Narnia and Watership Down and The Ranger's Apprentice series. Sometimes, they have not liked what I want to read with them - one of them might complain about it being boring - but in the end you can just see the positive effect it has, as the family bonds are strengthened.
My oldest is now in college, but we talk almost every day, and my second is a junior in High School, but he recently told me I was his best friend, and I replied, in all honesty, that he was mine. They interact very well with each other and care for each other. That sort of bond is built on every little moment where you work through the differences and learn to enjoy each other. You could even point that out to your kids, talk with them about how they like to read differently and how they can enjoy each other's style as a break from their own, and they can also enjoy the wonder of seeing their sibling's uniqueness. It is pretty cool how each of us is unique and different, and kids can learn to see that as a positive, joyful thing.
I do have "dates" with my children, times when I take one of them and we go out for breakfast or lunch or shopping or catch a football game. But much more of the time, we value doing things together as a family, over separating into smaller groups. I come from a group oriented culture (first 16 years of my life), and I could count on one hand the number of times I had alone with my dad. I then lived for 18 years in the more individual oriented American culture, followed by back and forth between different cultures and the US for the last 15 years. I see value in both, but feel that the best balance gives preference to group times, with only occasional (once a week?) individual times with each kid. For daily routines like this, I'd definitely favor the group.