Heirloom is not a type of vegtable. it is a class of many vegtables. A heirloom is something passed down for generations unchanged.
heirloom tomatoes for instants are a class of tomatoes that have been virtually unchanged for many generations like:
black krim, black seaman, brandywine, beefsteak, white beefsteak, german johnson, white belgium, polish giant, snow white and hundreds of others
heirloom corn would be:
indian corn, hopi corn, bloody butcher, golden bantam, etc
heirloom carrotts are:
Danvers half long, tendersweet, little finger.
A heirloom is of the old, before everything was genetically altered, like early girl, celebrity, and tasti-lee but unlike heirlooms they have last names lol I will introduce you to 3 of them now.
early girl (VFF)
celebrity (VFFNTA)
and tasti-lee (VFFF)
Any V means it is verticillium wilt resistant, F is for fusarium wilt strain 1 resistant, 2 FF means strain 2 as well but no 3rd F means not strain 3
tasti-lee is resistant of all strains of fusarium
celebrity is resistant to verticillium, the first 2 fusarium, as well as N= nematodes, T is tobacco mosaic virus, and A is alternia.
The advantages of each depend on what you grow, where your area is, if you grow in the same plot year after year, and many other things.
the truth is many of the heirlooms are harder to grow, but is so much more worth it for the flavor instead of quantity production.
Some of the new hybrids taste just as good..........but..........................I know I always have a but..............
The seeds from a hybrid, even if thats all you grow will not make another plant for you next year like the one this year, it is too genetically confused, 10 seeds out of those tomatoes can every one make a different plant from the other.
if you dont grow but one breed of heirlooms, or grow them far apart(several hundreds of feet), the seeds from them will be cross pollenated as well, now wont they, and the seeds will not be true to breed, no longer heirloom seeds
Side note: If you ever plant seeds from all of these crossed up tomatos, or a friend has a tomato plant that is just by far the best you have ever eaten, you can keep this plant alive virtually forever, turning it into thousands.
A cutting from a tomato plant will root in 10 to 14 days in a pot of soil, just keep it out of direct light, and soil damp. ready for transplant in 2 weeks. They will even grow roots in a jar of water in your kitchen windowsill. With this knowledge you can make several cuttings in the fall, take them indoors to root, grow all winter, turn these into cuttings in the spring, and plant many many plants from a single one. I still grow a yellow tomato every year like this, and have for 20 years. The original came from my great grandmothers garden by my mother. I have no idea of its name, dont care, it is a very low acid, round delicious yellow tomato, that I hope to keep alive as long as I live. If one thinks about it, my plants are more than 40 years old, and kept this way. Now that is an heirloom tomato, LMAO The secret is not keeping all your eggs in one basket, I have had my plants in the house die before over the winter, Dog tore them up and ate them lol. Because 1 my mother had some, and 2 I have taught some friends how to do this, and have given them some of my clippings before, and they still loved them. I was able to retrieve some of them back. it really only takes 1. I grow many varietys like this, it isnt the same breed of plant, it is the exact same plant that my great grandmother had in her garden.
Dont be scared to plant many types of tomato, or plant the F1 generation of seeds that come out of them. You may just stumble onto the next best tomato winner, or they may grow huge plants with nasty little hard tomatos. Thats why there is over 600 heirloom tomato varieties to start with. Then they make enough with clones to start experimenting with manual self pollenation, and line breeding to lock in the genes, to get consistant fruit every time, then they name it, and sell seeds from it.
I intend on stocking up on LOADS of these seeds 
