I'll try to explain the idiocity of most RGB mods with basic-intermediate tech talk:
First of all RGB signals transmitted to TVs are standardized, signals transmitted to arcade monitors are not. When you do a Neo Geo "bypass" mod (or many other popular mods that were not conceived by someone remotely familiar with video signals) you're typically wiring the video DAC's high-impedance (resistance) output directly to the TV input (low-impedance). This is how the MVS connects to a high-impedance load such as an arcade monitor, but it is completely incorrect to connect the DAC directly to a low-impedance load such as a TV or monitor. When you connect a low-impedance load to a high-impedance output, you get a loss in signal amplitude because the output impedance (here around 200 ohms) and the TV's load impedance (75 ohms) form a voltage divider that attenuates the signal. This makes the signal dark, because again the signal levels are standardized (0.0V is black, 0.714 is white).
The only reason this bypass mod works at all for people is because the DACs output a signal 3-5x larger than the signal arriving at the TV is supposed to be, and many TVs have the ability to crudely compensate for bad signals. If the signal level is too high (as I suspect in the pictures above), you get brightness/contrast issues.
The NG's DAC is just a logic chip functioning as a binary weighted voltage source, so the output's full range is ~3 Vpp, the same voltage range that the logic chip's outputs swing. The correct TV level again is 0.714 Vpp... Huge difference! This is a big part of why the colors are wrong--The TV can only compensate so much. Since RGB signals don't have any sort of frame of reference a TV is pretty much working blind, it can only put some basic gain control into effect, and not every display can even do that, leading to inevitable clipping/distortion (usually oversaturated colors) and brightness issues (low contrast).
Also since the DAC is created using a logic chip which isn't very good at sourcing current (it's meant to drive other logic chips often with 100k+ ohms input impedance), and because they don't want the output's current to have any influence over the voltage (creating non-linearity), they chose resistor values that were just low enough to reasonably drive an arcade monitor. Later with the AES the DAC's load became a voltage-divider that divides the 3 Vpp signals down to the correct 0.7 Vpp and feeds them into the Sony CXA RGB encoder (this is also a high-impedance load so its presence minimally affects the DAC).
When you directly connect the TV to the DAC, the 75 ohm load (low impedance) attempts to draw more current from the chip than it can provide, which drops the voltage = more non-linearity because the DAC can't supply the correct voltage, plus this puts a strain on the chip was wasn't designed for this. All bad. The DAC is only "strong" enough (it can only source/sink so much current) to drive a high-impedance arcade monitor (1k ohms) or the RGB encoder (probably 10k ohms). Again a TV is 75 ohms, 12 times too low. 75 ohms is standardized across the video industry and is essential for both amplitude compatibility between devices and also to maximize signal integrity for long cables (minimize reflection/ghosting, ringing, maximize power transfer). Some further reading (mathy): "impedance matching", "characteristic impedance", "transmission lines".
Putting it all together:
The only way to properly drive a TV (or most computer monitors with 75 ohm termination, or broadcast monitor without the option to disable the 75 ohm terminators) is to take the 3 Vpp DAC signal, divide it to 0.7Vpp and send it through a video amplifier with a gain of 2 (the CXA does this internally) so the final output is 1.4 Vpp, then send that through a 75 ohm resistor out to the TV so that the 75 ohm R at the output and the 75 ohm R at the display divide the signal to the precise 0.7Vpp amplitude desired at the TV input. If the video amplifier has too large of a DC offset for the amplifier to comfortably handle, series ac coupling capacitors can remove the offset from being delivered to the load, and reduce the current requirement. Alternately since the DAC's direct output is very large at 3 Vpp, instead of dividing it to 0.7 Vpp you can divide it directly to 1.4 Vpp, and send that through an amplifier with a gain of 1 (so its just a voltage buffer), then again out the 75 ohm resistor to achieve the right signal amplitude. This way has the benefit of not needing voltage amplification, which relaxes bandwidth requirements and improves noise figures.
The CXA already does it the first way, and it's internal to every Neo Geo console. The video quality isn't as good as it could be however because the amplifier in the CXA has limited bandwidth (as does everything), probably around 6 MHz. To achieve sharp pixels with the Neo Geo you need ~10 MHz of bandwidth, and this can be achieved with any modern video amplifier such as the ever popular THS7314. If you have a high-end display it wouldn't hurt to use a HD video amplifier (typically 30 MHz cutoff), these can be purchased for only a couple dollars now.
Do it right and it will work every time on every display... Obviously few modders understand what they're doing, and that's why they're all doing it wrong.