Biggest differences to me is that Google seems to handle natural questions like "how do i..." in a "smart" way whereas ddg seems to be more altavista like in that your keywords have higher weight rather than trying to outsmart you. Another difference is that Google is much better on local search thanks to its strong bonds with Google maps, like checking opening hours. For anything not maps related DDG has been my default for can't even remember how many years, over 5.
There are a bunch of these. !a forwards to Amazon, !w to Wikipedia, etc.
But I agree. I check on DuckDuckGo, if I can't find what I'm looking for, most of the time, adding !s finds it. If not, I go back and switching to !g.
It's the opposite for me. I use primarily google, but when the results suck (which is quite often), I switch to duckduckgo to obtain a sensible search.
Often with technical searches the DDG results seem better.
As to rerun the query, that's what the back button is for. Simply hit back, add your bang and enter. Most browsers keep that page in cache so going back is pretty quick.