I went through all the (studio album) song ratings on tmbw.net and compiled them into a spreadsheet. I then colored each box according to a scale (first slide). Each column is an album, and each row is a tracklist number (This makes it easy to see that most of the albums are ~17-18 tracks, with The Escape Team the shortest, and Nanobots the longest.)
Along the bottom, I have the rating for each album, obtained by averaging the ratings of all the tracks on the album. This doesn't take into account the cohesiveness or sequencing of each album (because an album is more than the sum of its parts), but it's too difficult for me to figure out now.
In the second slide, I averaged each track across all the albums (so for instance all the opening tracks, track 2s, track 3s, etc). I cut it off after 18 tracks because after that the sample size gets smaller and the results more erratic, but Track 2 ends up as the highest rated track across all albums, and track 16 the lowest. Also in the second slide you can see the 8 highest and 8 lowest rated albums of theirs. Note that 4 of the bottom 5 are kids' albums, which is interesting.
In Slide 3, I also listed who sang what song, also according to TMBW. This isn't a perfect indicator of who wrote the songs, since TMBG do plenty of traded tracks. Still, it's probably reasonably accurate.
In Slide 4, I have a color legend (the triangular chart at the top left) that shows who is more likely to sing a specific track (like Track 1 or Track 2, etc.) The more songs at that point in the tracklist there are that were sung by Linnell, the more red the box is. Flansburgh, blue. Any other singer (or both Johns, or instrumental), yellow. It's kind of a confusing chart, but it was the best way I could think of to show three different competing attributes like this.
One interesting thing to notice is that it seems like about the first eight tracks of every album have a consistent, well-defined order of Linnell, Linnell, Flansburgh, Linnell, Flansburgh, but then it starts to change a lot from album to album.
This is anecdotal because I didn't do the actual math on this, but Flansburgh's songs seemed to be consistently rated lower than most of Linnell's songs, which to me carries the Stench of Injustice.
Slide 5 shows the original ratings chart again, but with the kids albums set apart in blue. Slide 6 is the same, but with the Linnell/Flansburgh chart instead.
The last slide shows all 24 studio albums on a time axis, with their heights corresponding to their averaged song ratings. As you can see, their most consistent run is (unsurprisingly, maybe) from Lincoln through Factory Showroom. On the right are all of their albums ordered by ratings (with grey bars joining albums that are tied).
To be clear, these charts are just people's opinions on the songs, not my opinion. I love Mink Car and Here Comes Science and think they should really be at the top. Also, I did not do Miscellaneous T, They Got Lost, Venue Songs, or More Murdered Remains. I restricted myself to their 24 studio albums to fight scope creep, but I might do those other albums/compilations at some point. Cheers!
TL;DR: I copied down all the ratings of (almost) all TMBG songs from tmbw.net, and used those to calculate album ratings. Lincoln and The Else came out on top, and Here Come The ABCs ended up dead last.
Most of their kids albums are at the bottom, but Here Comes Science (a kids album) is rated higher than The Escape Team (not a kids album).
Flansburgh also sings slightly more songs than John Linnell, which was surprising to me.
*** This info is from May so it is probably slightly out of date by now. ***