You can definitely be successful with either solution. The first advantage of Leaflet that comes to mind is alternate tile providers. Google obviously uses their own map tiles (the images that are patched together to construct the map view), but using Leaflet you can use any provider you want. We used Mapbox in the video, but there is also OpenStreetMap, MapQuest, and Bing.
All of the providers have different licensing policies, so using Leaflet means you can choose the one that works best for your needs.
I'm sure that is not an exhaustive list of things to consider, but I hope it helps.