The problem is a lot of them do different things globally.
Some initiate, some save, some just deal damage.
First I'd like to break them up into groups and determine why each is the best of their group.
Ranged Missile
A champion that sends out an ability at a long range for global/semi-global impact.
Deals damage can initiate and can set up a kill from across the map. 3 second stun is insane. While not the best ability in all the categories, it's in all the categories.
Semi global, but deals the most damage and can hit all in it's path. Most full global ults lose a lot of effectiveness due to difficulty of hitting post a certain range. Lux ult is never effected by this and is the most reliable of all these abilities.
Orrns is the best initiation tool and is just better than Namis. Faster, hits twice, can be redirected.
Easiest to hit goes through all units, only does damage.
The second most powerful initiation tool of the group. Very slow, and easy to miss.
Deals good aoe damage, but since it's and execute and can't go through units makes it just worse than EZs in most cases. Rarely the reason Jinx earns the kill.
Super slow can easily be tanked.
Long Distance Dash
Champion must move across the map not teleport.
While at first a targeted dash may not seem great, Noc has 2 globals, the blind can cause disarray, disengage fights and save allies. Nocs blind is incredible powerful as it impacts the player not the champions, which is usually better.
Not targeted, but moves fast and is unstoppable. GREAT for taking fights or rotating as you can move your team very quickly. Hard not to give ti to Kled.
Can save an ally and has a huge knock up zone, problem is it requires an enemy to be in danger or to dive wildly first.
needs set up to do it, and probably shouldn't be doing it, but still that shield cannot be ignored. certainly better than the ones below despite being the shortest range in this group.
Better than Asols in all ways and adds a wall.
Very slow hard to land must be clear of all obstacles your better off with Kleds.
Very weak compared to the rest of these. Slow and does nothing. However being able to go over terrain and having it as a basic ability gives it a lot more power.
**Global Impact **
Champions that can impact almost anywhere without moving. That cannot be body blocked.
Karthus A tough call between Raka and
Karthus, at the end of the day though. Karthus demands you to build items or he get's pentas. Sorakas can have little impact at times as the one she saves can still die if they are just caught out.
Soraka and Karth just outclass everyone else in this category. Global 5 man effects are just some much better than a skill shot you must land.
An instant GP ult.
Can certainly stop a fight or secure a kill with
Very precise can be very good, but we all see how hard this ability is to land.
Teleports
Shens needed to be nerfed many times due to the power of this ability. It saves/assist initiations/ has global pressure and usually better than TP (a summoner).
Free range to go anywhere and reveal all 5 champions is uber strong. Better than Ryze, but just moves TF and that's it. Shen has more power since he shields and can join the front line.
Just a better Tahm ult.
being able to do what TF does ,but with an ally makes it better, but not seeing what around can make it a death trap.
With that who do I think is the best of the 4?
4th
: Ashe is the most versatile, but not the strongest.
3rd
Karthus has too many counters.
2nd
Nocturne has the blind, but the effects of the ult can be very lackluster and usually end in your demise.
1st
So Shen would be the best global ult as it's safe, strong, very good impact, and versatile.