A TBC will correct timing errors that are inherent in analog tape playback. You'd probably recognize timing errors visually as wavy-ness (i.e.; not straight) in vertical objects in the image. Most of the stand-alone TBCs also have proc amp controls that would allows for phase, contrast, luma and chroma adjustments.
Thinking about it more, using an S-Video cable will help eliminate Y/C delay, which has the affect of shifting chroma slightly to the right of where it should be. S-Video (aka Y/C) transmits the luminance and chroma portions of the signal separately instead of together like a composite signal would do.
Using a different or newer NLE won't make any difference. It's the capture codec you choose that can make a difference. Most people would use DV NTSC (or PAL, depending on your country) since VHS resolution is only about 240 lines.
-DH