As you have noticed, there are differences in the CSS classes and the styles in both versions, but the version that you are using is a rather old (and not supported) one and I would personally recommend that you modify your custom CSS, so that it could fit the new styles of the controls.
Notwithstanding, with "Classic" render mode you could set the DateInput-EnableSingleInputRendering property of the date picker controls to "false", which will reverse the rendering to older version, but once again, this is not recommended and it will be better if you modify your custom CSS.
Do you want to have your say when we set our development plans?
Do you want to know when a feature you care about is added or when a bug fixed?
Telerik Feedback Portal
and vote to affect the priority of the items