If you look at the mid-tier large cities, those between 600,000 and 2 million (to draw an arbitrary distinction), you can see how much more quickly Western cities have grown over the past few decades. (These charts only include cities that are in the top 100 for population from each Census, so cities that were too small to make that cut show empty data for those Censuses.)
Philly and Detroit and Baltimore have risen and fallen. A slew of Western cities have risen and risen.
As a percentage of change over time, the picture is slightly different. Charlotte, N.C. has been one of the few east-of-the-Mississippi rivers to see growth decade after decade. Cleveland and Detroit have seen the most collapse since 2010, and both have consistently gotten smaller. (New Orleans grew from 2010 to 2014, in part because Hurricane Katrina decimated its population between 2000 and 2010.)
Being politics junkies, we were curious what this might mean for, you know, politics. We pulled data for the top 20 largest cities for the last 50 years and compared rate of population change to how partisan the city's home county voted in each presidential election. In theory, the bigger the city's population, the more Democratic -- given the patterns we see elsewhere. But there was no strong correlation between rate of growth and voting relative to the rest of the country, in any of the five decades.
In other words: Big west-of-the-Mississippi cities getting bigger (as in, say, Texas) may not turn those cities into Democratic strongholds. After all, they've been growing steadily for half a century, and that certainly hasn't happened yet.