Full rotation with all skills at rank 1 :
Shen : 230
Zed : 165
So indeed, if you whiff every skills you have, Shen costs more.
Let's look further now, wha about energy refunds (which all energy users rely on).
Total refund posible in 1 rotation with all skills at rank 1:
Shen : 10-210 (net cost between 220 and 20, expected cost of 180)
Zed : 0-40 (net cost between 165 and 125, expected cost of 145)
So if you actually land your stuff, both champions bear similar costs. As soon as you land your taunt on more than 1 champion, it costs less early game as Shen for a full rotation.
Obviously, costs change with levels, so let's do the same 2 things with max rank spells.
Full rotation with all skills at level 18 :
Shen : 230
Zed : 125
Total refund posible in 1 rotation with all skills at level 18:
Shen : 30-230 (net cost between 200 and 0, expected cost of 120)
Zed : 0-80 (net cost between 165 and 85, expected cost of 125)
The values don't really change as you level up, actually. In a suboptimal case, both bear similar costs, in a disastreous case, Zed still holds the cup, and in a perfect case, you still null-value as Shen, while Zed still uses like 65% of its energy.
The one criterion I didn't touch on, up until now is time. So let's see how fast they will run out of energy in an abysmal case (nothing lands), ok case (you land you key spells and whiff the rest) and perfect case (all those 5-man taunts are worth a lot).
"Level 1" Shen cost : 23 energy per second.
"Level 1" Shen refund : 1-18 energy per second.
"Level 1" Shen net cost : 22-5 energy per second (expected 19).
"Level 1" Zed cost : 27 energy per second.
"Level 1" Zed refund : 0-3 energy per second.
"Level 1" Zed net cost : 27-24 energy per second (expected 25).
So early in the game, the tables are turned for once. Zed costs more energy across the table since he has very little access to its energy refund mechanics very scarcely.
Level 18 Shen cost : 40 energy per second.
Level 18 Shen refund : 3-27.5 energy per second.
Level 18 Shen net cost : 37-12.5 energy per second (expected 25).
Level 18 Zed cost : 23 energy per second.
Level 18 Zed refund : 0-17 energy per second.
Level 18 Zed net cost : 23-6 energy per second (expected 16).
However, come late game, Zed's energy costs are much less limitating. Hi W being up much more often simply means that his energy isn't all that gated anymore.
N.B. for expected values, I assumed that Shen would land 2 autos between Ki Strikes, one with feint on, one with it off and would land his taunt. Given that he's in lane these numbers seem very conservative. Come late game, I assumed 2 persons taunted and 2 AAs between Ki Strikes.
For Zed, I assumed he'd land all his Shurikens refunds, and miss all his Shadow Slashes refunds. I still assumed he would hit the Shadow Slash on the enemy for the 2s CDR. Come late game, I assumed he'd stil lland all his Shurikens refunds, and that he would still mis all Shadow Slashes refunds. However Iassumed he'd hit 2 persons with his Shadow Slash, and hit 1 more after (for 6s CDR total).
One point I didn't take into account would be CDR itemization which skews toward Zed because the refunds are gated by his Living Shadow uptime and Living Shadow has a flat CDR reduction when you hit Shadow Slash. I don't think it changes the conclusion in any ways however since it mostly come into play late game
In conclusion, until late game arrives, Shen's problem is as limitating as any other energy user. The only point where Zed can truly faceroll is lategame, but at the same time we have to wonder if that has to do with their roles. Zed is a squishy assassin that relies on mobility to survive, so he probably won't be able to just stand in the fray and spam spells. Meanwhile, Shen's job means he will stay alive longer than most, which compensate for the higher cost over time.
TL;DR : Shen got 99 problems but energy costs ain't one.