It’s in the hindsight of history that the differences that seemed significant at the time proved to not be. On the economy, both were mainstream neo-liberals. The best example is TARP. Obama inherited and continued TARP, but it’s also what he would’ve done anyway. Obama extended the Bush tax cuts for everyone earning below $400,000. On foreign relations, both were aggressive on terrorism. On immigration, their policies and rhetoric were similar, with Bush possibly being more liberal. (Bush strongly supported the Comprehensive Immigration Reform Act of 2007, which would have given everyone illegally present in the US on January 1, 2010, a permanent visa and pathway to citizenship.)
The two had different rhetoric on guns, religion, and abortion, but very carefully preserved the detante on these social issues by not proposing any significant legislation affecting them. On energy policy, both supported fracking and coal. (Obama had some last minute 2015 environmental regulations, which were quickly rolled back by Trump, but they clearly aren’t a priority seeing as how he waited until the last year of his presidency to act.) On healthcare, both had significant measures to expand coverage. (Bush’s Medicare Part D was a $50 billion/year program, while ACA was estimated to be $95 billion/year.)