I tried different settings and the games seem to be capped at 31 FPS. The Rebirth patch doesn't work for me and crashes the games.
Any fix for this?

Thanks

Both games are capped at 30 fps for gameplay at default.

Dino Crisis Classic REbirth caps the gameplay at 30 fps too.

Only Dino Crisis 2 Classic REbirth has 60 fps gameplay support.

Try Lossless Scaling and see what happens.

I use it to x2 mode, so I got 60 fps. Game become smooth. Also I tried x3 mode, it good too but have some glitches and artefacts around character. In my opinion the best is x2 mode for DC1 and x3 for DC2.

What does x2 mode mean?

x2 frame generation mode in app Loossless Scaling. It means that base fps will be doubled. If you have in game 30 fps, then after enabling frame generation you should get 60. Aso is good variants is x3 (triple) frame multi generation.
There also x4 mode. It is good for high refresh monitors. Even for fun you can enable x5-x20 modes as well.