Fresh is generally best, but is only available in season. Frozen is nearly as good, and is available year-round. Canned is OK for some purposes, is available year-round, and is usually cheaper than frozen. Dried works for some vegetables, and when it does, is usually the cheapest option.
And yes, I’m aware that frozen is usually fresher than “fresh”, but it’s also frozen. Freezing degrades the texture of many vegetables, sometimes significantly so.
We always have a bag of frozen peas and a bag of frozen corn for ongoing use. Peas in particular are nice for a “different” garnish.
I frequently buy boxes of frozen okra. I put them in the freezer and at some point my gf incorporates them into a meal. After years of my doing this, she just recently caught on. (all along, she just assumed she was buying okra, I guess. One day it dawned on her that she had never purchased it, yet we always seemed to have some on hand)
Canned carrots and green beans and even potatoes are fantastic for toddler finger food, easy to transport, easy to store. We go through a ridiculous amount of canned vegetables ever since having a baby.
This.
I just hate the homogenous texture. Take green beans: they are uniformly blah when frozen, and once in the mouth disintegrate into a green mush. When I prepare them, they’re never a uniform size and I like to cook them until they still have a goodly ‘bite’ within…that is, bring to the boil for maybe two minutes, simmer for one, then onto the plate.
As they are, doused in a little vinaigrette dressing or butter with finely chopped garlic…eeeeeeelicious. 
Sure, but canned green beans are perfectly fine, as long as you don’t over-cook them. Personally, I’d be hard-pressed to identify canned from store bought fresh in a double-blind test if everything else was controlled, like size.
Unless I am making something specific (pumpkin to go under a hunk of beef in the slow cooker or every vegetable imaginable for my huge vat of pasta sauce destined for the freezer) the only fresh veggies here are onions, tomato and garlic - sometimes a bag of carrots if I am in a munching mood. I’ll pop out to buy mushrooms on the day if I want them though also keep some dried ones in the pantry.
Cans include tomatoes, baked beans, mexi beans (kidney beans, corn kernels and salsa), creamed corn, pie apple and chick peas.
Frozen include mixes of various veggies and bags of separate items, nothing with sauce or other additions. I like the spinach that comes in a box as loose leaf over the blocks of finely chopped. Frozen berries too.
This way we eat a much greater variety and amount of vegetables than our fridge would allow us to store and nothing gets slimy in the crisper. I grow herbs, lettuce, tomatoes and blueberries.
Canned beans here are pre-cooked, and even mushier than the frozen. They are truly revolting.
Maybe you guys have a better quality of processed vegetables than we do. 
I only get mushy frozen veggies if I overcook them, I use the microwave mostly and have plenty of al dente beans and crunchy broccoli. The carrot bits in the mixes are always a bit soft but carrots do that
Peas! I forgot about those. We have frozen peas.
Nope, in the US canned green beans are raw (possibly blanched) green beans. Usually they are in inch long slices, or sliced lengthwise (“French style”) and packed in water.
The very reason I buy frozen green beans (or any veggie) is because they still have a little crunch to them. The canned stuff is the stuff that’s all mushy.
I have a salad for work lunch which contains fresh vegetables: spinach, mushroom, cherry tomatoes, red onion, cucumber as well as peppadews from a jar.
For dinner, we often have frozen broccoli/cauliflower but sometimes frozen beans. I’ve never come across frozen pumpkin/squash/asparagus/courgettes so we’d always have those from fresh.
Typically I do a weekly grocery shop and we’ll have fresh veggies with dinner at the beginning of the week, then when they run out, we’ll have frozen.
I’ve never found frozen veggies to be mushy or lacking texture, unless they’ve been cooked too long. Certainly with the broccoli and cauliflower, it’s a different texture to when I steam from fresh, but it’s still very pleasant.
We only eat corn occassionally, but when we do, it’s equally likely to be frozen corn on the cob, frozen loose corn, fresh corn on the cob, canned corn kernels or even creamed corn. Dammit, now I really want corn.
Fresh veg is more expensive, requires quick use, and there’s no evidence it’s more nutritious. I get potatoes, squash, onions, Brussels sprouts, and the occasional root veg like parsnips fresh, that’s about it.
I almost always use canned beans (kidney, black). Dried peas and lentils (for soup). I keep my freezer stocked with frozen broccoli, kale, spinach, collards, and snap beans.
And that about covers all the plant foods I eat. Except white rice, coffee, and tea.
This is incorrect. The process of canning cooks the beans way past blanched.
It depends strongly on the season. During the summer we eat from the garden (tomatoes, squash, peppers, beans, snow peas, eggplant, etc.) and from the farmers’ markets near us. In the winter we get the stuff available at the farmers’ markets, fresh veg from the store if the prices is reasonable, but more frozen. Never canned.
We’ve found that the brand of frozen veg is a significant indicator of quality. Birdseye frozen beans are pretty good, but store brand frozen vegetables are not nearly as nice and sometimes mushy. Frozen Brussels Sprouts are not bad either.
And we freeze corn from the summer (we buy 4 dozen ears) and some other things like fava beans. I don’t know how these count.
Around the house on a regular basis:
Canned - niblet corn, creamed corn, beans of all sorts, julienned green beans, beets, tomato products (diced, crushed, stewed, sauced, pasted, whole, Ro-Teled, etc.), peppers diced, whole and adoboed, pickles of all sorts
Frozen - peas, spinach, pearl onions, various potato products
Dried - potato products (hash browns, flakes), beans of several sorts
Fresh - Living in SoCal, we can pick up fresh veggies at the farm stand near school any time. On hand right this minute are lettuce, onions, chilis, potatoes, cabbage, brussels sprouts, sweet potatoes, carrots, green beans, peppers, cucumbers
The only canned goods I buy are beets, pumpkin, tomato sauce and paste, and canned pineapple. For veggies and fruit, I prefer fresh, but I’ll buy frozen. I grew up on canned veggies and I now find them flavorless and too mushy.
I turned away from cans when I had corn at my MIL’s 30 years ago - it tasted fresh and she told me she used frozen. That was that. I’ve always got bags of veggies in the freezer.
Canned: kidney beans, tomatoes for sauces, corn, beets (love pickled beets straight out of the can, even better with a hard-boiled egg marinated in the juice for a few hours), Asian pickled vegetables and, oddly, seasoned greens.
Frozen: peas, mixed stir-fry veg. I like peas with rice, the mixed stuff works well when I can’t be arsed to do anything but some ramen with veg.
Fresh: carrots, cabbage, anything salady, green & yellow beans (except in three-bean salad, then canned is best), Brussels sprouts, broccoli, zucchini, etc.
I’m going to slide this up to Cafe Society since it seems mostly about food.