Sissy,
Hello & Welcome to the Forum!

I'll be honest and tell you straight up that I am biased in favor of the Transformer/Analog control system over the Lion Chief Remote. 
All of my O scale electric trains are Transformer controlled.

The Lion Chief Remote System uses a handheld remote controlling an individual locomotive.
link to Lionel Product Announcement:
http://lionelllc.wordpress.com/2013/02/25/new-product-spotlight-introducing-the-lionchief-remote/
(I suggest you read the comments posted with the product announcement.)
With the Lion Chief you will need to run locomotives that are equipped with matching receivers to the remote.
That rules out running Pre War or Post War, MPC or later era Locomotives that you would be able to run on your track with a straight transformer control system.  That is IF your son continues with his interest in trains and wants to expand his layout.

The Polar Express Locomotive looks good pulling it's Passenger cars, but will look equally good in the future pulling a string of rail cars, should Santa decide to leave a car or three 'neath the Christmas tree....

Happy Rails!
Dave