To find the answer I did some Science.

Method

I slept for 96 hours then I consumed each of 25 foods and 5 beverages until my character's hunger moved from famished to properly fed, and his thirst moved from dehydrated to properly hydrated.

For each food I then multiplied the food's weight by the number of units required. I also multiplied the food's rads by the number of units required. (Though not essential for this question, I also looked at how many hit points each items heals.) This gives us useful numbers to compare the foods:

• Pounds to feed: the total weight required to feed a famished character
• Pounds to hydrate: the total weight required to hydrate a dehydrated character
• Rads to feed: the total rads required to feed a famished character
• Rads to hydrate: the total rads required to hydrate a dehydrated character
• HP per Pound: how much healing it provides for the weight (again, not directly needed for your question but useful when choosing between the food options)

The Candidates

There are seven farmable crops: carrot, corn, gourd, melon, mutfruit, razorgrain, and tato. All of these address hunger; only melon also addresses thirst.

Of the many craftable food items, only two meet your criterion of being completely crop-based. Both of these address hunger and thirst:

• noodle cup (one razorgrain, one dirty water)
• vegetable soup (one carrot, one tato, one dirty water)

For completeness I included:

• 16 other craftable food items with meat ingredients
• dirty and purified water
• all three Nuka Cola varieties

Short Answer

Noodle cup.

Longer Answer

• Noodle cup is the best crop-based option overall.
• If you have noodle cup, there's no reason to carry purified water.
• If you don't mind consuming a few rads, supplement with mutfruit.
• If you don't mind using meat, supplement with mirelurk cake when you have the ingredients.

The raw data for all food items tested is below.

Reasoning

Thirst: Noodle Cup

You'll get thirsty much more often than you'll get hungry—in part just because that's how the game works, and in part because healing items (stimpack, Rad-X, RadAway) add thirst. So efficient hydration is critical.

Purified water and noodle cup are the two most efficient rad-free thirst items: from dehydrated to properly hydrated in just 3lb. They weigh the same (0.5lb) and heal the same (40 HP).

Because noodle cup also helps hunger, and everything else is equal with purified water, noodle cup wins.

Hunger: Noodle Cup (with side dishes)

Noodle cup is the best item for hunger as well. Not because it's the most weight-efficient—mirelurk cake wins there—but because:

1. If you're using noodle cup for thirst anyway, it will automatically help your hunger at the same time for no added weight cost.
2. While it's not the most weight-efficient food item (3 pounds to feed), all of the more weight-efficient food items either add rads (uncooked fruits and vegetables) or require uncommon meat ingredients (iguana, squirrel, stingwing, deathclaw...).

Mutfruit is a good backup item for hunger. It's as lightweight as any other plant crop, and has the lowest radiation: 0.8 pounds and 16 rads to fully feed you.

Parts of the map are rich in mirelurks. If you're willing to look beyond plant crops and have the ingredients (mirelurk meat, mirelurk egg, oil, and razorgrain), mirelurk cake is the most weight/rad efficient food item among the 25 items I tested.

Dirty Water

The drawback of noodle cup is that it's not common to find dirty water in the Commonwealth. But in survival mode it's an easy item to make for yourself.

Empty bottles are one of the most common items in the Commonwealth, especially in bars, restaurants, and breweries. Take an empty bottle to a body of water and you'll see the option to fill the bottle. This will give you one dirty water.

Bonus Facts: Healing

Mirelurk cake is by far the most efficient healing item among the 30 I tested: 1390 HP per pound. It's around 300% more efficient than the next closest items (Nuka Quantum and Iguana on a Stick), and around 700% more efficient than the seemingly-awesome Deathclaw Steak and Mirelurk Queen Steak.

This is another reason to keep it in your inventory as a backup item if you have the ingredients.

Raw Data

Pounds to feed

• 0.4: mirelurk cake
• 0.5: iguana on a stick
• 0.8: carrot, corn, mutfruit, crispy squirrel bits
• 2: deathclaw steak, mirelurk queen steak, roasted mirelurk steak, stingwing filet, yao guai ribs
• 3: baked bloatfly, bloodbug steak, grilled radstag, noodle cup, radscorpion steak
• 4: mole rat chunks, mutant hound chops, mutt chops, ribeye steak, tato
• 8: vegetable soup, gourd, melon
• Infinite: razorgrain (no food value)

Rads to feed

• 0: (everything not listed below)
• 16: mutfruit
• 24: carrot, corn, gourd, melon
• 40: tato
• Infinite: razorgrain (no food value)

Pounds to hydrate

• 3: water, dirty water, noodle cup
• 6: nuka cola quantum
• 7: nuka cola, nuka cola cherry, vegetable soup
• 8: melon

Rads to hydrate

• 0: noodle cup, purified water, vegetable soup
• 24: melon
• 30: nuka cola quantum
• 35: nuka cola, nuka cola cherry
• 42: dirty water

HP per Pound

• 10: gourd, melon
• 20: nuka cola, tato
• 40: dirty water
• 50: nuka cola cherry
• 55: vegetable soup
• 80: baked bloatfly, mutt chops, noodle cup, purified water
• 100: carrot, corn, mole rat chunks, mutfruit, razorgrain
• 110: ribeye steak
• 120: grilled radstag, mutant hound chops
• 138: roasted mirelurk meat
• 150: radscorpion steak
• 164: yao guai ribs
• 185: deathclaw steak
• 200: mirelurk queen steak
• 210: bloodbug steak
• 260: stingwing filet
• 340: crispy squirrel bits
• 400: iguana on a stick, nuka cola quantum
• 1390: mirelurk cake