If I can only take one of them, should I take cherry bomb or doom shroom?

The Doom Shroom and Cherry Bombs have similar purpose so are nearly interchangeable.
Taking the Doom Shroom as a base these are the advantages and disadvantages it has agaisnt the Cherry bombs:

Advantage:

• Higher range (7 by 5 compared tot he 3 by 3)
• Cheaper (125 sun instead of 150 during night)

Disadvantages:

• Destroys the lily-pad it is on or renders the ground unusable for 3 minutes (Which might just as well be permanent)

So it all comes down to situation and personal skill but personally I would go for the Cherry Bomb. The reason for this is that when placed on the front a cherry bomb can clear half the enemy wave. In combination with the Cattails (which you should pretty much always use in pool levels)(or other multi lane shooters) this works perfectly. The whole range of the Doom Shroom is overkill and only needed when you already made such big mistakes you might as well restart the level or if it's literally the last wave that is coming. because if you use it sooner outside of a lily pad it will effectively cripple your defenses by one tile for the entire level and if you use it on a lily pad it loses it's cost effectiveness bonus reducing the only upside the Doom shroom has it's unnecessary large range.

The only levels I would see Doom Shrooms as a better choice is when you forgot to use plants that can shoot backwards or otherwise defend against digger/bungee zombies or Imps. But then it would just be better not to forget picking those plants instead of the Doom Shroom.