I have both of them installed with the fanpatches and resolution patches, but even before that, I get awful FPS on the map and save/load screens, if I were to guess, about 15fps in them. It's still useable, since neither of the screens require any kind of reaction or precision, but it's kind of annoying. Anyone else have this problem or know a fix?

Try to set graphics to use DX9 instead of default DX7. You can do this using "Preferences" withing game's menu or directly editing INI files.

It already is set to DX9.

What "fanpatches"? Killap's Restoration Project 2.3.3 or just Unofficial Fo2 Patch 1.02.31? Did you installed resolution patch too? Wrong move! HighRes Patch is included:
http://falloutmods.wikia.com/wiki/F2RP_Technical_Info
... and installing it after "patch" could mess your game.

Change DX9 mode to "4" in ddraw.ini file:

[Graphics]
;Set to 0 for 8 bit fullscreen
;Set to 4 for dx9 fullscreen
;Set to 5 for dx9 windowed
;A dx9 mode is required for any graphics related script extender functions to work (i.e. fullscreen shaders)
;Modes 1, 2 and 3 are no longer supported
Mode=4

Under [Misc] make sure multiple processors core function is disabled:

;Set to 1 for force fallout not to use multiple processor cores even if they are available
SingleCore=1

If above didn't work then you can experiment with:

;Set a number of milliseconds to idle each input loop
;Set to -1 to disable
;Set to 0 to idle only if other processes are waiting for processor time
;Set to 1 (or some higher number if needed) to prevent 100% cpu use
ProcessorIdle=1

Killaps, and I don't think I installed another patch with it. Will try those solutions now.

The game is already set to use singlecore, I have set the DirectX mode now and will test it out.

*edit* Changing that didn't fix anything and only killed the 2x scaling, making the game tiny on my monitor. I guess I'll live with the slowdown.

Both are Killap's. And after checking only Restoration Project has integrated HighRes patch. Looks like Unofficial Patch requires it. Newest version 4.1.8:
http://www.nma-fallout.com/showthread.php?181743-Hi-Res-Patches-for-Fallout1-amp-2-amp-the-BIS-Mapper

If all install looks correct then check you AnitVirus soft and/or Security Suite. Maybe there should be some exception for "fallout2.exe" or something...

I use the restoration project. Still the problem didn't change when using the different DX9 setting.

Well, then check your security soft. In my Eset NOD32 AntiVirus I've got exceptions for "fallout2.exe"...

How would my antivirus affect this? I don't think it is messing with Fallout, to be honest.

AV soft is checking every running executable. I had problems without exception in Eset NOD32 AV. Make test and set exception in your AV or Security Suite (AV + Firewall).

If it will not help then copy saves to safe place and reinstall Fo2 and latest Restoration Project.

Ah! I forgot. INI file for HighRes is stored NOT in game's folder:

; Affects Windows Vista/7/8 and above. Allows hi-res patch settings to be changed without admin privileges
; if installed in the "Program Files" directory.
; When UAC_AWARE=0 the hi-res patches settings will be stored in the game folder as usual.
; When UAC_AWARE=1 the hi-res patches settings will be stored in the users roaming app data folder.
; For Vista this is usually "C:\Documents and Settings\'your user name'\Application Data\Fallout2".
; For Windows 7/8 this is usually "C:\Users\'your user name'\AppData\Roaming\Fallout2".
UAC_AWARE=1

Make changes to that INI file...

The .ini file in the AppData folder (f2_res.ini) is wildly different from what you described, in fact, the fallout2.ini from the actual game folder is the one that fits with your descriptions.

Because I was describing INI file in game's folder before. I totally forgot about UAC because I've disabled it at the beginning of using Win7. Sorry.