For your mission, you'll do fine with either. That's what consumer camcorders are designed to do. Check the comparison here: http://shop.panasonic.com/compare/?itemNbr=HC-X900K&itemNbr=HC-V700K
. There are lens differences, sensor size differences and others. One big one is the viewfinder on the 900. Tracking fast moving kids may be much easier when using the viewfinder -- especially outdoors.
If I were shopping for a camcorder now, the two you listed would be on my short list. I would also add the Sony HDR-GW77 because it will take great video, but it is designed to be rugged and waterproof. You will feel more secure setting it on the birthday table to attend to a kid that spilled their milk. If it gets bumped off the table, a kid sneezes on it or beach sand gets blown onto it, nothing is lost. Because of the form factor, it will be more likely to be in your pocket, purse, pack or beach bag.
Another on my list would be the Pansonic "bridge" cameras. Last year's FZ150 and this year's FZ200 are exceptionally good at both video and photo. I bought one for my wife.
Geeks and reviewers get hung up on technical issues and features. For example a lot of reviews will kill a camera because it does not have full manual control. Shooting kids needs full automatic and good image stabilization. You don't have time for manual if you want the "cute moments". In today's market all cameras above $400 or $500 will take very good family video. In the end, it is who is shooting not what they are shooting with.
For what it's worth, I have an expensive camcorder much like the 900 and a pocket camera that is video capable called the HX9V that only cost $320. It get far better video than the big one because it is more likely to be with me and less likely to be noticed by the subject. The output on a 55" TV is nearly indistinguishable. (Sony's current version is the HX20V.)
You won't make a mistake, unless you get one so complicated you never learn how to use it.