Improvements can vary greatly by title, however.

https://youtu.be/ftBB3ffc5A8

Earlier this week, we were surprised by reports that the new Version 4.5 beta firmware for the PlayStation 4 Pro offered an unannounced "Boost Mode" promising "improved gameplay, including higher frame rates, for some games that were released before the introduction of PS4 Pro." The folks over at the excellent Digital Foundry have now put that new mode through its paces, finding frame rate increases of up to 38 percent on unpatched PS4 games.
Those frame rate improvements are very dependent on the specific title in question, though. Destiny for instance, is locked to 30fps in its code, and thus gets no benefit from Boost Mode. An intensive online shooter like Battlefield 4, on the other hand, can stay at a solid 60fps in Boost Mode, without the frequent frame-rate dips that can occur during a 64-player match in base mode.

Many games seem to see the same modest 14 percent bump in their frame rates in Boost Mode. That coincidentally matches the 14 percent faster clock speed that the PS4 Pro's GPU has over the original system (911Mhz vs 800Mhz), suggesting that the additional processor cycles are helping on GPU-limited games. Boost Mode doesn't seem to make any use of the 18 additional compute cores available in the PS4 Pro, however—for that, you need a game-specific patch to be coded by the developer.

Games that are also limited by the CPU in the original PS4 can see even bigger performance improvements in Boost Mode, thanks to the PS4 Pro's 30 percent faster central processor. A game like Assassin's Creed Unity jumps from a janky 22 to 24 frames per second before Boost Mode to a more consistent 30fps with the feature activated. And Project Cars sees a very noticeable 35 to 38 percent increase in performance.

While games that are explicitly patched with the PS4 Pro in mind still seem to perform best, Boost Mode seems to provide a major frame rate improvement to a wide variety of older PS4 titles. Check out Digital Foundry's write-up for more information, including a detailed video that goes into some depth on the test results for additional titles.