The difference is that any kind of elements you are going to introduce in your model has different degree of freedom (DOF), As an example one shell element may have 18 dof or less or more depending from the number of nodes. A plate element could fave 12 dof as a minimum (one displacement and two rotations) or more if you introduce high order element with dof in curvature for example.

I think that it is really important to select the right element in order to computationally optimize the running of the model. More element more dof more time consuming.

The accuracy of the results depends on the element´s node number and also on how many elements have been considered into your mathematical model. For example, the rectangular element of five nodes gives more information to you than the rectangular element of four nodes does. Have you been interested in specific zones of the structure, you would increase the number of elements just over there (other zones could have less amount of elements because they have not complex behavior or it is well know) Evidently, the computer spends more time as soon as either the number of nodes or elements increases. So, I recommend you select the element and mesh which fit in your model, give the results with the required precision and make your computer spends less time on resolving it.