The Max 6-6 Version of TwinNote
TwinNote's more radical cousin, the Max 6-6 version maximizes the visibility of the 6-6 pitch pattern (whole tone scales) through the use of hollow and solid noteheads.

In this version of TwinNote, triangle notes that point up are always solid, and those that point down are always hollow, regardless of their duration. This reinforces the 6-6 pitch pattern that is already present in the shape of TwinNote's noteheads — the regularly alternating pattern found in the chromatic scale:

The benefits of a more visible 6-6 pitch pattern are that notes become even easier to identify and intervals become even clearer and easier to distinguish from one another. This is illustrated on the Scales and Intervals pages (select "Quarter Notes, Max 6-6 Version of TwinNote").
In traditional notation and the standard version of TwinNote, hollow and solid notes are used to distinguish between half notes and quarter notes. But consider that whether a given note is hollow or solid is its most visually apparent quality. It is much easier to see if a note is hollow or solid at a glance than to determine its position on the staff. Wouldn't it be more effective to use hollow and solid notes to make it easier to identify a note's pitch? And also to emphasize the 6-6 pitch pattern, maximizing its benefits?
In order to distinguish between half notes and quarter notes, half notes are given double stems in the Max 6-6 version of TwinNote:

Aside from using hollow and solid noteheads for pitch and double stems for half notes, the Max 6-6 version is the same as the standard version of TwinNote. All the other rhythm and duration symbols are the same as those used in traditional notation.
Which Version of TwinNote to Use?
When compared with the standard version of TwinNote, the main disadvantage of the Max 6-6 version is that it would be harder to learn both it and traditional notation at the same time. Because it uses hollow and solid notes to indicate pitch instead of duration, switching back and forth between the two systems "bilingually" would be much more of a challenge. Conversely, one of the main advantages of the standard version of TwinNote is greater compatibility with traditional notation.
Musicians who need or want to learn to read traditional notation may be better off learning and using the standard version of TwinNote. For musicians who do not want or need to learn traditional notation, the Max 6-6 version may be the better choice, given its advantages in terms of pitch and interval clarity.
Why Two Versions?
Each version of TwinNote has its advantages. It seems better to offer both versions and let musicians decide which one to use based on their own needs and goals, rather than try to prescribe which one should be preferred. Luckily with notation software it is almost as easy to produce sheet music in both versions as it is in just one. Of course, when the Max 6-6 version of TwinNote is being used this should be indicated at the top of a score.
For further discussion see the Music Notation Project's tutorial on Using Notehead Color for Pitch.
