In this scenario kruskal's algorithm will run faster than prim's. The time complexity of kruskal's algorithm is
O(E log E) <--(time taken to sort E edges) + (E α(V)) <-- find set and union operations
Given that edge weights are uniformly distributed over half open interval [0,1), we can sort the edge list in O(E) time using bucket sort (see CLRS Bucket sort).
So now the running time of kruskal's MST algorithm will become
O(E) + (E α(V))
where α(V) is the inverse ackermann function whose value is less than 5 for any practical input size 'n'. (ref wiki)
so, the running time of kruskal's MST algorithm is linear, where prim's will still work in O((V+E)log V)