CSUR was designed to be completely independent of the Cities: Skylines vanilla road system to optimize user experience. This means that you can build your city using only CSUR road assets, which is also the recommended way to use it. This also indicate that we cannot guarantee compatability between a CSUR road asset and any other road asset not developed under the CSUR standard or software framework, although we have tried our best to maintain such compatibility. CSUR roads as were published on Steam Workshop are able to connect to all vanilla tiny, small, and medium roads without model glitches. When CSUR roads are connected to vanilla highways, the junction will sink below the road surface and vehicles will seem to be floating when passing the junction.
There is no silver bullet. The same applies when you're trying to choose the best tool to build your dream city. CSUR and its lane-based idea do have inherent limitations compared with the vanilla roads, which are mainly the side effects of not using nodes in the game. For example, building a diamond interchange can be difficult and building a diverging diamond is even harder. A non-exhaustive list of known issues are listed in this page. But generally speaking, if you play CSUR the way it's supposed to be used, everything just works.