I honestly never saw the sword beam as an overpowered attack, mostly because there were a few limitations placed on it. Most of the time it was only possible with the "special" sword of the game, either the Master Sword or the Four sword sometimes. After that the beam is usually weaker than a regular sword attack and you require full hearts to be capable of it. After all these requirements normally most players do not have the sword beams for very long.At least for most players who are reckless enough to be hit once or twice in a dungeon.
The spin attack I almost never use, mostly because of the charge up time that I do not like at all. It typically leaves me vulnerable to attack from enemies while I try charging it up. The only other alternative is to charge it on the far side of a room and then slowly strafe up to the enemy. That really slow pace on the way over to the monster kinds annoys me, so I usually just leave the spin attack behind and use regular attacks which I think are much more reliable. The only time I ever used it was in the early parts of ALTTP when the guards were a little too strong to take on normally and I did not have enough hearts to fight them off. So I would charge up a spin attack and wait for them. Later I discovered throwing pots at them was slightly more effective so I ended up dropping the attack then as well.