I safety/video boated on the Apurimac for a couple of months a decade ago--spectacular scenery, magnificent whitewater, and real potential for accidents. As noted above, there have been some, and there are very few user daysrelative to commercial runs in the US. Have to say I was NOT impressed with the way I saw companies manage risk on the river. Some guides were very, very good, and some were in over their heads, and I didn't see the attention to detail and consistent decision-making that creates an atmosphere of safety. A lot may have changed in the last ten years. If you go that route, though, I'd take any recs on companies pretty seriously. Should also mention that much of the clientele for the Apu in the fall is Israeli kids, fresh out of the army. Nice folks, but not exactly a family vibe. Pretty sure it's different other times of the year, though. The Apurimac's a GREAT trip, and you'd base out of Cusco, which in itself is the experience of a lifetime.
Never paddled the Tambopata, but what I've heard jibes more with the 3-4 good fun and natural beauty descriptions. Maybe a better fit for a family?