The one thing that truly made stamblade the beast it is in solo-PvP, is it's ridiculously strong defense and mobility toolkit, which remained strong through out the entire ESO lifecycle. Shadow image and cloak compliment each other perfectly and when combined with dodge and snare removal tools allows stamblades to survive through just anything. Having such a ridiculously strong defense to fall back to, lets them build for so much damage other classes won't even dream about. Plus, while they lost several class buffs in Elsweyr, they got back Minor berserk and Minor endurance via universal skills. WHich means, the only thing they lack in comparison to pre-Elsewyr NBs is Major Defile and Major Fracture, but some good stamblades moved on to using other combos outside Surprise attack and Incap, which means they basically lose out on nothing. And the primary strength of stamblades solo is the ability to choose their fights and never be forced to fight in unfavorable situations unless they want to.

The tier-list by @BohnT and other great PvPers, is only applicable for top-tier PvPers, which means it is about how the best player of their respective classes stack against each other. It only takes into account the people who literally knows their classes inside out and their experiences. S-tier stamblades does not imply that the average stamblade will fare better than other classes in PvP. Neither does it mean that a good stamblade is guaranteed to win all duels even if they commit mistakes. It simply means, the top stamblades will have an advantage in solo combat in difficult scenarios like 1vX compares to say A-tier classes like top magsorcs or top magplars. In the battle of bests, stamblades win out significantly. There is a reason for the last two years, every dueling tourney has been won by stamblades. This also reflects in 1vX, in which you will find that the best outnumbered fights by other classes have 1v10, who usually succumb with more players or if even a small organized group of other good players arrive. The best stamblade 1vXes have them going against high as 20+ players, and even if they don't kill everybody, they kill a lot more before escaping successfully than other classes who wouldn't even survive in that situation.

The reason why some people feel stamblades are low-tier, is because stamblade has a very different learning curve than other classes. Stamblades has an easier learning curve slope initially compared to other classes, due to Cloak. But after that, the mastering curve of stamblade is very steep and is a true test of patience and involves lots of PvP experience(and dying while at it) as well as very low reaction times, good decision making capability and high combat intelligence. The main reason for this is that inspite of stamblades having defense and offense capability, it is fully active in nature, defense a lot on proper positioning and changes in every scenario, unlike the high passive defense of say Templar or Warden and the easy offensive combo of Magsorcs. NBs have to learn to properly set up their fights in order to win, unlike say magplar, who can run in with Jabs,Breath of life and still be effective. Stamblade is a pure example of high risk, high reward.

Majority stamblades never go beyond the initial learning phase and the number of players who actually mastered it is far lesser than other classes. 99% stamblades don't know how to use Shadow Image effectively while a master stamblade knows that Shadow Image is far stronger than cloak as a defense skill. And I don't blame them, it is very hard to learn that skill, before you can even properly use it in combat considering it's limited time and positioning aspect. Result is that 99% stamblades get eaten up by equally skilled players on easier classes.

Just yesterday, I was on my Stamplar in Cyro and faced 5-6 man AD group consisting of mostly stamblades. Given how most dominion stamblades are, I killed every single one in a 1vX without feeling much pressure. They couldn't even escape the sheer pressure of Jabs while trying to cloak and dodge without any good.... Just a bit far away, a certain other AD stamblade was watching his brethren getting slaughtered without bothering to join in. Deciding to finish the 1vx on a nice high, I decided to attack him. I just couldn't manage to keep him in my Jabs, and he was straight up spamming Shade teleport. However he showed no sign of attacking me giving me no sense of threat and I managed to CC him, following up with Onslaught, Jabs. Just when he enterred execute range and I knew I had won the fight, he disappeared (I presumed shaded away again). Next thing I saw was my HP bar dropping ridiculously fast. I casted vigor and the templar healing ult Remembrance, which saves me against even zergs. This happened next.

This was on Nord templar with pariah and troll king with nearly 40k resists in execute. I had a 19k vigor and nearly 50k healing ult, which also gave me Major protection on me. I have fought many good players and survived the wrath of zergs. Not even very good magsorcs, magplars or any other class for that matter, ever managed to kill me on such a tanky build with a single combo, without even the use of healing ult. Yet, this stamblade had such ridiculously high damage that he drowned all my mitigation and self-healing with just his first combo without even bothering to use his class burst skill, while making a mockery of my offense as well. You can see from the death recap that he had packed 60k+ damage in just 3 gcd, which means over 20k+ dps, that is straight up crazy in a PvP scenario. This is the difference between a good stamblade and the average stamblade. No other class has such a big skill gap.