We often hear people and other real estate agents claim that houses in more expensive areas appreciate faster. However if you compare areas with significantly different prices, most often the appreciation rates track each other.
Sample Silicon Valley House Prices

The graph of Los Altos house prices and Milpitas house prices, shows two quite similar lines running parallel to each other. This is typical of areas in Silicon Valley. The rate of appreciation, expressed as a % of price, is quite consistent across different areas. A key aspect of this graph is that the y-axis uses a log scale.
Price Plotted Using A Linear Scale
Most house price plots use a linear y-axis scale.

Both line plots show a constant growth rate of 8%. Quickly glancing at the graph would give most people the impression that the upper line shows greater growth. However, when considering the growth of house prices, the growth is almost always expressed as a percentage. The upper line would look the same if it was plotting the total growth of two houses, each initially priced at $250K, rather than a single house initially priced at $500K.
The linear scale plot leads to the misconception that 1) “better areas” appreciate faster and 2) you had better hurry and buy a home because the growth is increasing.
Price Plotted Using A Log Scale
Plotting the same values as above using a log scale give a very different impression.

The above graph shows the same values as before, but plotted with a log y-axis. Both lines run parallel to each other and are straight. A quick interpretation would be that both have the same constant rate of growth, which is exactly what it shows.