Foxhack: I want to record some stuff from a game for a video but dunno what the best way to do that is.
The built-in capturing is extremely faithful to the original material. I think it actually captures the game in the native resolution without any filters applied, no matter how you play it - it may mean more editing but it also means that you have more control and well, simply more faithful material in the game's native resolution. Another thing is that (unless I'm mistaken) DOSBox' own capturing won't capture General MIDI / MT-32 music because that one is rendered by the operating system's MIDI synthesizer (or a custom one you may be using) rather than DOSBox itself (note that Soundblaster and Gravis Ultrasound are emulated by DOSBox itself so that should be included in the recording, same's true for emulated CD Audio I believe).
Fraps will capture DOSBox' actual video output, so if you set DOSBox to stretch the game to 1080p you will end up with 1080p video. You may consider this both an upside or a downside. I considered it rather good because it saves me a lot of effort during editing although it also means more stress on the HDD during editing. Another thing is that Fraps will capture your system's audio output so you will also get the MIDI music in your audio recording.
Foxhack: Also, I thought Fraps only captures full screen stuff.
Nope, it will even capture the visualization in WinAmp. FRAPS will capture both Direct3D and OpenGL output, no matter whether it's fullscreen or windowed. I think the only thing you won't be able to capture are DirectDraw applications, basically most old 2D Windows games.
I've tried a bunch of different recording tools for games over the years, the only one that has satisfied me so far is Fraps. I haven't tried Action, though, which is supposedly pretty much as good and cheaper for personal use.