I've been toying around with an all fourths D-G-C-F tuning (low to high) on a baritone uke - normally tuned D-G-B-E - by tuning up the B and E strings by a half step to F and C. This tuning really opens up the whole fretboard and it's become apparent that you can have a world of fun just by noodling around in this tuning. It makes everything interconnected.
The Irish tenor banjo fifths tuning of G-D-A-E is great for playing traditional tunes (single-note melodies) in first position where you utilize open strings as much as possible, but the reaches are too far to intuitively transpose to other keys when playing in different positions up the neck, unless you are way up there. The tenor banjo's scale length makes the fifths tuning too spread out for that. It is a tuning designed for the shorter fingerboard of the violin or mandolin.
A fourths tuning on tenor banjo would put all the notes under your fingers anywhere you are on the neck. It's like an equalizer that frees up the ability to play by ear and by feel. My main concern is that with fourths tuning - with only four strings - is that you lose some range when compared to the fifths tuning. For example, if I started with same open G for lowest string, it would take all the way up to the 9th fret of the highest string to play two octaves ("G-C-F-Bb tuning"), whereas in G-D-A-E you have that same two-octaves higher G on the 3rd fret of the highest string.
However, I don't think lack of range will be too much of an issue. Fourths tuning is the same tuning as used on bass guitars and many of the world's greatest bass players, including Chris Wood and Jaco Pastorius, do just fine with a 4-string bass. If I found that I definitely needed more range, you could always have a banjo neck made to accommodate 5 full-length strings.
It's almost unheard of to do this on 4-string banjo, but the fact that all fourths is the standard tuning for bass guitars at least means that there is at least some form of instructional material out there, if necessary. Some guitarists use an all fourths tuning as well, sometimes called P4 tuning. Stanley Jordan is probably the most well known guitarist who uses this tuning. He tunes his six strings E-A-D-G-C-F, so if I do D-G-C-F I'll be matching his 4 highest strings.
I'm not too concerned with having some more difficult chord shapes by using an all fourths tuning. I'd mainly be using it to play single-note, scale-based, melodic stuff and not full four-string chords, although I bet you can get some cool, weird, dissonant voicings. And finally, the all fourths tuning might make everything sound a little different but that is OK. The concept of music itself is the roadmap and it doesn't have to be instrument specific.