Yeah it's not just the perspective that the new tires are a superior design or whatever. It's that the old tires are wasted. Tires don't just wear out in tread, they also degrade in support/structure. Remember, tires are just like springs and they take a TON of abuse.
The new tires will be even better once you break them in and get the mold release agent worn off and get some heat cycles in them. Some new tires feel floaty at first & take a bit of use to get them "settled in."
Got some new tires for my mom's car years ago and she wasn't happy how they felt. Told her to just be patient and they'll get better. A few weeks later she noticed the improvement & asked how I knew that. Experience I guess? I'm a tire nerd (relative to the general population, not the smart guys who design them) and sometimes I know what i'm talking about?
Good on you for getting some new tires when you needed to. I'm of the opinion that tires and brakes are the most neglected parts of the car by most people. Ironically, they're the most important.