There is not a huge difference in my opinion. You will get a few more cassette cogs if going from 9 speed to 11 speed so you can stay in a more narrow range of preferred cadence. The more expensive bike will feel somewhat lighter when you pick it up by hand. A more expensive bike might come with lighter wheels and you may feel they accelerate a little quicker.
But as mentioned by others, for the most part the vast majority of performance comes from the rider not the bicycle. It is fun to ride a nice bike, but I've never felt at a disadvantage when riding my cheapest bike versus my most expensive bike, and my most expensive bike when new cost about 7 times what my cheapest bike retailed for.