This forum post discusses competition variance and poses a metric to quantify "leaderboard shake-up": https://www.kaggle.com/c/liberty-mutual-fire-peril/forums/t/...
The Public Leaderboards are very helpful though! When you have setup a solid local cross-validation pipeline, and the public leaderboard agrees with your local evaluation, then you can try a lot more algorithms and parameters, without using any submission. Especially when working in teams this is important as you may have only 1 submission every 2 days.
Also, the more advanced Kagglers can use leaderboard feedback to increase model accuracy: Cluster the data sets with objective measures. Apply a modifier (restaurants from this region get 0.95 x previous prediction) and look at the result. If the split between public and private is random, and your clustering is objective, then an improvement on public leaderboard should reflect in private leaderboard.