Things that like permanently moist soil should do especially well in containers. Peas, mints, leafy greens, brassicas, strawberry, and even celery and rhubarb. That's because at least the bottoms of containers almost never dry out. Always wet down there. That's the perched water table. Many plants don't like wet roots.

I tried tomatoes for a couple of years. My tomatoes used to get diseases if I did not crop rotate, in addition, I was using cover crops, sometimes the timing was off for tomatoes.

I had a niece without a yard, together we grew tomatoes, upside down in a bucket, she at her place, me at mine. We were both happy with the results.

Maybe not better than raised beds, but an alternative when I did not want to plant tomatoes in my raised beds.

All my veggies are in containers of one size or another..... bigger the better. Right now I have 3 tomatoes in a pot 3' across and that deep; one eggplant by itself in a 12" pot and two more in another 3' pot, they will share space with either cucumbers growing up a trellis; Peppers are individual in 12" pots. There are also lots of herbs, and even citrus and fig trees in huge pots. The most important thing is to fertilize at least once a month with a fertilizer appropriate to the plant.... no matter what soil you used. I like liquid best. And, I use organic potting soil.

anything that has small root mass will do well in containers.. bigger plants like tomatoes and peppers and tubers (potatoes) require large 10-15 gal minimum pots to do well. another problem is watering. big plants require a lot of water and that means daily watering which can be a pain if you have a lot of pots, not to mention frequently fertilizing them.

beets, carrots, onions, garlic also do well in pots and take up little space.1 square foot of space is enough to grow 12 garlic heads or onions.

For decent onion bulbs, the plants need to be separated by 4 inches. The full size bulbs end up shoulder to shoulder. No way are you going to get 12 of them in a square foot. I'm skeptical about beets as well. Might get two or three in a square foot, if you're lucky. But if you're after the greens and not the roots, go for it.

sorry meant to say 9 garlic, spaced out every 6 inches so that's 9 per sq foot if my math is right ;)

but ideally, you'd want a pot that is slightly larger than a square foot so you don't plant right up against the sides of the pot.

Tomatoes in my area are much better grown in containers than in the ground. Soil temps are slow to warm up in spring and it is never very hot in summer so growing these plants in containers maximizes the heat factor so we can actually realize some ripe fruit before the end of the growing season. Other solanaceous plants - peppers, eggplants - also do very well in containers for the same reason.

I also grow all my herbs in containers so I can manage the fast drainage and lean growing conditions most prefer. Except for rosemary. Grows too fast and too big to be in a container for very long.

I like to grow eggplants in containers (5 gallon). Hot peppers I grow in containers as well (2-5 gallon). Determinate or container or compact tomatoes grow well in containers too (5 gallon). Most herbs I grow in pots as well.

I have tried cucumbers and broccoli in 5 gallon pots but didn't have much luck. I've grown sweet potatoes in 5 gallon pots, but the pots are too small and the sweet potatoes will be small, long and twisted.