There certainly are differences between the Vado 3.0 and 4.0 which mainly deal with the level of the Shimano groupset (3.0 lower but still very functional), battery size, fork, etc. Probably the biggest difference between the 2 bikes is that the 4.0 is a Class 3 Speed Pedelec, where the motor provides assistance up to a top speed of ~28 mph. The 3.0 is a Class 1 where top speed with motor assist is ~20 mph. Class 3 bikes generally have a bit heavier duty components to cope with stresses at higher speeds. They can also tend to use battery capacity faster as wind resistance really hinders forward motion at speeds above 20 mph.
If you feel that you will be using your e-bike in a more casual manner, you would likely be very happy with the 3.0. If getting from point a to point b in the shortest time is what you are looking for, then the 4.0 would be your choice.
Either would be a fine choice for your first e-bike especially if your local Specialized dealer is a good shop. Nice to have the local support and great warranty.