The answer is fairly easy for anyone that has paid attention to Dragonball Z. The posters above can joke all they want, but they couldn't be more wrong. The difference of power ups between Z and Super is that the Power Ups in Z occured over time and were a result of either effort, deception, desperation or all of them. Per arc:
Saiyan Saga
Raditz anounced to Piccolo that stronger Saiyans were on their way to Earth. Vegeta and Nappa were much stronger than Piccolo and Goku at the time of their fight with Raditz. Vegeta would arrive in a year and in that year, the Z fighters were training to try to be prepared. They weren't, Vegeta and Nappa turned out to be stronger. Only Goku could match Vegeta. His power increase to almost defeat Vegeta came from work and training in otherworld. He even progressed
during the fight with Vegeta. Gohan's power potential has been established in the very first Z arc aswel. So his power boost later in the series didn't come out of nowehere. The power boost to defeat Vegeta came from pure effort.
Frieza Saga
The main attraction of the Frieza saga was the enormously powerful Frieza vs Goku. The strongest in the universe at the time. Vegeta, Piccolo, Gohan and Krillin weren't a match for his final form. Goku was also losing against Frieza. His power boost to even be able to fight Frieza came from 2 near death experiences (in the spaceship and when Ginyu stole his body) and training. See my reaction to nightbird's comment below for further analysis. So the power boost to defeat Frieza came form effort (training), deception(Frieza being stronger) and desperation (Krillin's death).
Android Saga
The big baddies were the Androids. Android 19 and 20 were stronger than Frieza was. How did the Z fighter get a power boost from Frieza saga to Android saga? Well, Future Trunks warned the Z fighters about the Androids and they had the time to prepare and train. When the Android's came, 19 and 20 were taken care of relatively easy. Then the deception came: 16,17 and 18, which were much stronger than 19 and 20 and according to Trunks, also stronger than their future counterparts. This deception was incentive for the Z fighters to improve. Piccolo fused with Kami, Vegeta went to the ROSAT with Trunks.
Cell Saga
Cell became stronger because he absorbed 18 and 17. He didn't get rediculously more powerful though, as he admitted Trunks would have defeated him is his USSJ form wasn't so slow. Then Cell announced the Cell games. In order to stand a chance against Cell, the fighters went into the ROSAT. So the power boost to fight Cell came from sheer effort over a long period of time (1 year training in ROSAT). Goku couldn't defeat Cell. Gohan got the power poost to defeat Cell from deception (Goku dying, Trunks being blasted) and desperation (16 dying). This triggered his SS2 transformation, similar to Goku's SS transformation. In total, the Androids were matched and Cell was defeated though sheer effort over time, deception and dedication.
Buu Saga
Majin Buu, who is stronger than Cell, hatched shortly after the Tournament. Piccolo, Vegeta and Goku's power boost at the beginning of this arc/saga came from the fact that since Cell, they've been training for years, putting in effort. So that explains their power boost. It is this saga in which Trunks and Goten got introduced, which seems to be the only thing Fj0823 can cite in favor of Super. And he's wrong, Goten wasn't as strong as Gohan and Trunks had a lot of trouble walking at 100G. A power boost is from X to Y, that moment established his power, it didn't give a boost to it. You might argue that their base strength is too high, but both have been showed training, so there's that: effort. And they were concieved while their father had a high base strength.
Anyways, continuing, Goku's power boost to match Majin Buu was his new SSJ Form
which he achieved through years of training (read: effort) in otherwold. Meanwhile, Gohan was training in the Kai's world. Some poeple think believe his power boost came from unlocking his potential by the Grand Kai and his dance. However, he went though a tough training with the Z-Sword. At the end of this training, he was shown to be able to handle the Z-Sword with ease. Goku had a little trouble lifting the Z-Sword. So that's that power boost to Mystic Gohan.
Then there is Super Buu. Super Buu outclassed Vegeta and Goku, which is why they fused. This isn't a power boost per character, but a fusion. That didn't work and that spawned Kid Buu. Vegeta/Goku didn't have a power boost to defeat Kid Buu and the Spirit Bomb that defeated him was aided by the life force of the Earth.
So the power boosts in this arc came from sheer effort (apart form Majin Vegeta, but that wasn't a permanent power boost). Also, every respective step in power boost isnt crazy big. Form X in DBZ allows the good guy to fight the bad guy, but not win. Then the power boost is needed.
And now the difference with the bullshit that is DBS:
Beerus arc:
One second, Beerus is manhandling SS3, the other moment he's a SSG holding his own, though no effort whatsoever. To top this off, his SSG form wore off and Beerus told him that Goku made the SSG power his own. So Goku got a powerboost basically out of nowwhere. To top it off, the magnitude of the power boost he got was bigger than any power boost in DBZ, and probably comparable to the power boost from Goku when he faught Raditz to SS3 Goku. This is where the series shot itself in the foot. Beerus is unfathomaly stronger than any Z foe, and that power is not the base for the rest of Super.
RoFrieza arc
Both Vegeta and Goku achieved SSB Through effort. Frieza went Gold also though effort. However, the magnitute of the power boost, again, from Frieza is an even worse insult, for just 4 months. The BS about this arc is that Frieza seemingly knew how strong he had to get to defeat Goku, which was SSB by the time. How could Frieza even fathom to train to that level, it is monstrously bigger than his strength at the end of the Frieza arc. It's like going form Yamcha to Vegito in 4 mothns. Not a single power jump in either Z (or GT for that matter) comes lose to that.
Champa arc
Cabba turned SSJ though no effort. There was deception and desperation though, as he thought Vegeta would exterminate his family. However, what is really poorly done in DBS and in also in the ToP arc is:
ToP/u]
The U6 Saiyans only get stronger through forms. It's like they say: hey I need to get stronger, time to get a new form! In DBZ, there were power boosts within a form before going to the next. Goku's SS got some power boosts before he went SS2, his SS2 became stronger over time before he became SS3 etc. The U6 saiyans have to growth or development, it's just trigger. Caulifla's SSJ forms came without effort, without deception, without desperation. Same goes for Kale. And to explain why this is utterly stupid, SSJ forms are a multiplyer of base strength. Directly transforming from one form to the other without increasing your strength is actually pretty dumb.
So tthe point is: whoever is Saying that power boosts always have been dumb in Dragonball are simply talking out of their ass. DBS is disgracefully bad in its handling of power boosts.
What on Earth are you talking about? You said yourself that this is the second time Krillin gets killed. The difference is the context. During his fight with Frieza, we see Goku struggle a lot, Frieza was winning. We then get one of the most critical but often forgotten moments in Dragonball history: Goku's Nightmare. While being drowned, he saw what would happen if Frieza were to win, he saw Krillin die, he saw all of his family and loved ones die... The Earth.. all of it. That gave him a power boost to at least fight Frieza for a while again. It wasn't enough, but it was a defining moment. Then, after he thought he had killed Frieza, he reappears and kills Krillin. His nightmare became reality. This is the context in which he became SSJ, out of rage, out of desperation, out of deception.