At face value the replacement you list would work just fine as the 600 mA rating just means that it is capable supplying power to more devices (like LEDs) than the 400 mA supply.
As an example if each LED in the fixture needed 100 mA (LEDs usually require much less than that so just an example) then the 400 mA transformer could power 4 and the 600 mA one could power 6. It's not really that simple as there are other devices in the circuit that need power too but you get the idea.
Another issue is that you have to be very sure what input power is required. The easiest way is to read the output specification on the original transformer but since you noted that the original transformer was missing you need to find another way.
If the LED fixture lists on it somewhere what the input requirement is then you can go by that. If not do a search on the web using the product name and model number and try to find the specifications there.
The hazard of guessing (incorrectly) is that you could supply the wrong voltage (AC vs DC), potential (too high of volts) or polarity (+-, if it's DC).
Tom
