The processor is the same. And while on paper the benchmark scores can be identical, the fact that the new SE has a smaller screen than the 11 and 11 Pro means that it will be snappier. I say this based on experience.
Anytime you shrink screen size, there is less screen to process. So, assuming the processor speed stays the same, the device with the smaller screen will be snappier. By snappier, I mean faster in terms of maneuverability. For example, when swiping between screens and quicker to initiate app swaps, etc.
This behavior is very easy to reproduce on a PC. Anytime you shrink the resolution, virtually every game will run faster and smoother.
This principle was also true with the original iPhone SE and more noticeable than most people imagine. I played with the original SE and my iPhone 6S side-by-side many times (same iCloud with same identical phone contents) and I can tell you for certain that the SE was ALWAYS snappier; navigating between screens was simply smoother and faster. This is an objective observation I made many times over the years.
My iPhone 8 was also quicker in navigating and responding than my iPhone X and XS.