Some cards reward you if you have more Prize cards left than your opponent, or if your opponent has taken a lot of Prizes. Several of these also happen to be among the strongest cards in the format, and I have seen fit to allocate entire sections of this guide dedicated to them.
While a Prize difference can occur naturally through regular back-and-forth attacking, there are styles of play that goad your opponent into taking the Prize lead and turning on your comeback cards:
Some Pokémon have weak or non-damaging attacks that discard cards from the opponent's hand or field. Examples are Stantler's Push Away, or a Minun using Sniff Out to loop Energy Removal 2.
If your opponent does nothing about them, they'll hemorrhage resources (unless they have Raticate), but if they KO your Stantler or Minun to stop those attacks, your comeback cards are now live.
Comeback cards only count Prizes taken. You may be behind on Prizes, yet significantly ahead on board, if you're able to beat your opponent's Pokémon to within an inch of their lives without KOing them. This can be achieved with attacks that let you choose which Pokémon to hit, or attacks that spread damage evenly across all the opponent's Pokémon.
The Rai-Eggs deck utilizes this game plan, and understanding it is the key to playing it well. You can hold off taking early Prizes by spreading damage with Split Bomb and Zzzap, fall behind in Prizes mid-game and rely on Scramble Energy to power more Split Bombs or Metallic Thunders, and finally pull ahead late-game after milking Scramble Energy for all it's worth.
Why wait for your opponent to take Prizes if you can give those Prizes to them?
The easiest and most popular way of feeding your opponent Prizes.
Note that you can use Extra Energy Bomb even with no Energy in the discard. This might be necessary if you want to turn on a naturally-attached Scramble Energy, or if you know your opponent has Sceptile ex δ but hasn't gotten it out yet.
If you Swoop a heavily damaged Basic Pokémon for another with less HP, the new Basic can be KOed immediately.
Jirachi HL is a common Swoop fodder, as its HP is relatively high and Make a Wish damages itself.
If you have Basics with Poké-Powers, you can play Cursed Stone to chip and eventually KO them.
One example is Camler, which plays both Unown E and Cursed Stone despite the seeming anti-synergy.
Rainbow Energy can KO a Pokémon with 10 HP remaining.
This trick is most commonly seen in Bombchamp, as it not only plays Rainbow Energy to begin with, but also has Electrode ex to get back the spent Rainbow Energy from the discard pile.