I am playing the D3D version of the game since the 3DFX version crashes constantly. However, there is a problem. Whenever text appears on the screen, either for dialogue or a pickup notice, the framerate takes a massive drop. It is kind of annoying. Has anyone encountered this and, if so, is there a solution? I have seen the slowdown on Win XP, Win Vista and Win 7.

Have you tried using dgVoodoo for 3DFX instead of the provided glide DLLs (which I think are an older nGlide version)? It might prevent the crashing in 3DFX mode. I think I read that there are level scripting issues when using the D3D in this game on modern machines, like doors not opening and you getting stuck in the level.

I will try the other wrapper, but I am not that hopeful. From my tests, I did not encounter the Elijah Hotel bug or any of the door bugs in the D3D version. I do remember the bug, though. I have reduced the game's resolution to 640x480 as a workaround because the drop goes from 60FPS to 30 FPS, which is still playable. Bear in mind that this issue is on the operating systems I listed. I tested the game on Win10 with 3DFX and had no problems. Likewise, I dug up my old Requiem disk, installed it on an XP machine, patched it and installed nGlide independent and had no problems at all. I think the problem is with the DLLs used for the GOG release. I am still testing. I would normally take a jab at GOG for insufficient compatibility testing, which has become a problem with them over the past two years, but I vividly remember how absolutely grouchy this game is to get running...even on Win 98 native.

There is a post where people have had issues with the GOG provided glide DLLs and they replaced them with those from the latest version of nGlide to get it working, so you could be right, they could be sub-optimal DLLs for the game.

For XP, the DLLs are not the issue as the 3DFX version still crashes. I suspect that something is in the EXE causing that particular issue. I will keep investigating to see what I can get done.

After further investigation, I have concluded that there is no resolution for this issue. I tried substituting a No-CD Patched 1.3 version of the 3DFX executable, which causes an Explorer.exe 100% CPU usage hang. trying any other fix causes the same errors.

As for the framerate drop in the D3D version, I suspect the included OGG DLLs and the player might be the cause, but since I can keep the game playable despite the bug, I see no reason to investigate at this point. Both my old retail copy and the GOG version are still playable, so I have no real reason to complain too much.

Alright, this is going to be one heck of a necropost, but so be it. I had the exact same problem.
tl;dr-
Install the widescreen FOV fix.
The one I found (that worked) was here.
It'll bring up a menu asking for width, then height. This is your screen resolution, or at least, the one you want. Input it, then just hit enter to close it.
Note- I did this with a "pure" install of the game from GOG. DGvoodoo2 flat out stopped the game from running. Configuring it simply through the provided n-glide, and running the d3d.exe in the main folder after a fresh reinstall had it work.
Boom, fixed.
The only other issue now is it slows down while doing conversation audio from NPC's sometimes (random), and occasionally the controls will lock up (say, after dying).

The game worked fine on 3dfx mode, but the resolution and stability was very low. HOWEVER, text showing up didn't have any problems. On D3D, and only on higher rez, text on screen or bringing up the powers menu halved the frame rate. With this fix, the frame rate is fixed, BUT, it does shrink your in-game menus on every other pause, for whatever reason.

I will check this out to see if it works.