What scale is it?

since the Polar Express is a fictional train, it would be difficult to judge the scale of a model, but that being said, a Berkshire type locomotive (the type depicted in the movie) will usually have drivers in the 68"- 72" range, while small switchers sport wheels as small as 30"-35" (B&O).

i would guess the Lionel model is O27 sized which can be as small as 3/16" scale (1:64).

Same way with Lionel's postwar GE 44-tonner. The real locomotive is about the size of a caboose. But Lionel made it bigger so it would look good with other 0-27 locomotives and cars.

I'm assuming you've got the train set Polar Express.  The locomotive and cars are not true 1/4" scale, but are what's best referred to as "traditional size."

Lionel was, and still is the master of "selective compression," (or "selective expansion" in the case of the 44 tonner...)in shrinking down dimensions so the locomotives and cars still look "right" on the very sharp O27, O31 and O36 curves. 

This selective compression is not consistent for height, width, length and may vary from product to product, so there is no way to determine the actual "scale" of these products.  It seems to be mostly based on visual appeal by the Lionel design engineers.

Rusty

My middle son (34) who is very into toy trains, too, was playing with his neice and nephew as they drove remote Thomas and he drove the Polar Express asked the same question of me. 

My answer was that its scale is"one fun-ty-forth."