A new oven may very well be more efficient than an old oven, but if both were properly preheated, there should be no difference in results between two ovens set at (say) 350ºF – but therein lies the rub. Ovens are not precision intruments, and are often shipped with thermostats that are not perfectly accurate. My oven can be reset – e.g., to read “350ºF” when the temperature is actually 360ºF – to give the same results as some other oven at a given temperature. This makes the transition between ovens a little easier, and I suggest you check your owner’s manual to see if your oven will do this. If not, then yes, you’ll have to adjust the set temperature for your recipes to work properly.
It seems to me that 350 degrees is the same regardless of oven and its age. I have a thermometer inside our older oven to monitor the temperature. Its a good way to accurately see if the thermostat is working properly.
It really depends on what the recipe is you are cooking.
Some meats don’t need to be cooked as long because they are leaner.
Some old cake/cookie/pastry recipes need to be altered slightly because the flour we use is finer and more specialized than the flour available generations ago. Recipes no longer call for sifted flour and there is the self rising flour and other such wonders of modern baking.
It isn’t the oven that changed but the ingredients.