I have both types on various banjos. They are my favorite tailpieces. Both work great for me - depending on the instrument.

On my Williams/Burlile Kenny Ingram model bluegrass banjo, I use a tensionator (oettinger style). That instrument sounds more dynamic (to me) with the individual string adjustment. I replaced the OEM Presto wth the tensionator.  Presto would be the obvious choice on a pre-war copy mastertone banjo.  After using the tensionator for a while, I temporarily switched back to the presto. But I missed the tensionator - so that is definitely the set up I prefer.  The back-and-forth just served to confirm that I really like the tensionator.  

I use a reproduction Oettinger from the UK on my favorite open back (a custom Nashville Banjo Co 13" Governor model). These are beautiful reproductions (a LOT like the originals). I LOVE the Oettinger in that one!

I've owned several 4-string original oettinger tailpieces on vintage B&D banjos,  Individual string adjustability really does allow you to fine-tune the tone of each.  

But I definitely prefer Presto tailpieces on most of my Bart Reiter banjos. Presto tailpieces have their own sound that is unique and very appealing on some instruments. 

My advice is to try both and see your yourself. There really is no substitute for that.

Do you want to effect the downward pressure of the strings - from bridge to rim, at the bottom of the banjo - all at once, or individually?

I think of an Oettinger style tailpiece as a mechanism for adjusting the tone quality of each string, individually; something that isn't possible on all-at-once tailpieces.

As far as "equalizing the tension of all strings," I don't know; maybe that's a thing, but I've always associated string tension with string gauge.

I have an Oettinger style tailpiece on one of my banjos. Besides its uniqueness for individual string tonal adjustment, one of the other things I especially appreciate about it is the graceful way the strings lay in their own groove, to the way the string rolls out at the end of the tongue - very elegant, and a smooth run for nylon strings (nothing to get hung up on.

When I met with Béla Fleck to discuss low-tuned banjos I saw that he had an Oettinger style tailpiece (tensionator) on his cello banjo, so obviously he found it to be a useful device. There's definitely something about Oettinger style which have made them such a valued item, above and behind the fact that they look so cool.

HI the real Oettinger has in difference to Presto mor material- is heavier- with an Presto sometimes is a wom sound - but is a questoin of taste

I have banjos that have both styles of Ottinger tailpieces and also Prestos. Both styles are original vintages. Also have a RB-800 that has a beautiful engraved post WWII variation.

I love the Ottinger for its looks and ease of use. My original thoughts on these many decades ago was that they were for fine tuning strings, like what one sees on a violin. String tension never came into my mind.

The sound that comes out of a banjo is dependent upon so many variables, bridge, strings, type of head, and tail piece, it is near impossible to say which would have the best tone.

My Ottinger sounds fantastic on a 1927 RB-3, but sounds terrible on a 1926 Ball bearing RB-3. Same for the 800. The Ottinger definitely improves the sound. Switched it out once with a Gold presto and the sound died. Might be the extra mass.

Best thing about an Ottinger over a Presto is changing strings. Does not get any easier.

jbalch , Paul Roberts , and Alvin Conder,

When you prefer the Oettinger, how do you have the fingers set?
Are all the fingers the same height, or in stairsteps with the bass string being closest to the head, or something else?

Can you “flesh out” more specifically what you’re looking for, or what changes in the sound when you adjust each finger, than what sounds “better”?

Anyone know of a comparison demo online? I saw 2, and they really never played the banjo, nor compared it to any other tailpiece on the banjo, just talked!)

Of course every banjo and every player taste is different, but it would convey some examples of how the tailpiece is used and its effect.

I’d appreciate any more clarity because, as we know, the Oett style tailpieces are expensive, hence the post and trying to find out what they might be able to do and deciding if it’s worth it to me.

Baconfine , which were you saying has the warmer sound, the Oettinger or the Presto?

On the comments (incl. mine), about the “purpose” of the Oettinger style being to individually adjust strings to equalize string tension, it’s from an article (attached) I had come across by CC Richelieu, founder of Richelieu Banjos, on the Oettinger style Tensionator tailpiece. (The Tensionator tailpiece was, I believe, essentially the same (different appearance) as the Oettinger, and made by Richelieu, though the name, and maybe design, was later used also by ABM. (Someone correct this if it’s not accurate.))

In it he says, “The only purpose of the Tensionator is to control and equalize the string pressure…”. It’s a quick read and worth it. The difference of view/experience is also why I posted, for player views/experience.

Yes, I think the Oettinger style is super cool too! And elegant!

Rockyjo

This explains how to set up an Oettinger:

oettinger.co/tailpiece-set-up.php

If you remember your high school trigonometry, think of the string as the hypotenuse of a right triangle. In the case of a banjo with an Ottinger, you have a unique right triangle for each string, unlike other tailpieces, with which you have only a single triangle for all strings. 
Increasing the angle (moving the arm closer to the head) will increase the pressure down on the head (SOH CAH TOA, in this case, SOH). Decreasing will decrease the pressure. More pressure = louder. So on a tenor tuned CGDA, with will be the extreme case under banjos, the high A string is under crazy high tension and exerts more pressure on the bridge, and so is much, much louder. So the Oettinger lets you even out the volume of the individual strings, like setting pole pieces in a guitar pickup. It doesn't affect the tension on the string itself - screwing the arm down will obviously raise the note, which you will then retune. A given string of a fixed composition and diameter over a constant length (that is, nut-to-bridge) will produce a given note at only one tension. Otherwise, stringed musical instruments would be a real adventure.