Will I get higher quality mp3's with the -k switch (lame 3.97b3), or is the commandline -V2 --vbr-new - %d fine?

That's actually not so easy to answer without ABX tests, heh. I just tested it a bit to see how much the bitrate increases with -k in VBR, but it was surprisingly little. That could mean that -k steals bits from the "definitely audible" range and utilizes them for the "maybe audible" range instead of just adding bits, which can lead to worse overall quality. But the process of hearing and lossy encoding for our hearing is too complex to answer it in such a general way. I would just say, stick to what's known to be good; the recommended settings.

For V0 - V2 (where -Y is not forced), increasing the lowpass frequency/disabling the lowpass filter (-k) will* increase the bitrate. How much the bitrate increases is determined by how lame treats the extra high frequency noise (if there is any at all).

Using -k at V5 - V3 won't effect the bitrate hardly at all because of -Y. Doing so will force lame to smash more audio bandwidth into the same amount of space... maybe (the reason why I hate the -Y switch, ATH plays a big role in that 'maybe')

Of course the only way for you to find out which is better is to ABX. But with -k you will end up with more high frequency stuff (that you may or may not be able to hear anyways).
<opinon>But considering using -k should increase the bitrate anyways, it would probably be easier to just use V0 instead.</opinion>

* Increasing the lowpass dosn't always increase the bitrate, the opposite can happen with certain close lowpass frequencies. I can't remember how to reproduce it at the moment though.

I don't think that the -k switch is recommended. Once I asked what exactly the -k switch changes in case of quality. Responses were: Lower bitrates also have to concentrate on high frequencies people can't hear. The resolution is, there are maybe quality decreases in low bitrates, because the lower frequencies aren't encoded as well as lowpass filter is active...

The reason WHY the increase of bitrates isn't as high as expected could be that there aren't so much higher frequencies.... Or lame tries (because of the -V X parameters) to safe filesize and ignores the requierements for higher bitrates (=> quality decreases)

The reason why the increase of bitrates isn't as high as expected (at least at V2 - V0) is because V2 lowpass is 19khz and maximum that psymodel allows is 20khz, so the extra 1khz will not affect the bitrate much (or not at all at -V0, 'cause the lowpass is already at 20khz)