You didn't give us much information to go on. Where are you, what gardening climate. Are the plants indoors or out, have you transplanted them or are they still in the original containers?

Im in Memphis, TN. They are outdoors. I'm doing a container garden, the 5 gallon bucket.

Okay, for us to be more helpful you need to use specific descriptive words when describing the problems your plants have. You used the term 'plenty' when describing sun light and watering, 'plenty' is a relative term as compared to 2 qts. of water every three days. Also, describe your potting technique, including: soil used, drainage, holes in the pot, etc.

The information you've supplied us with is sketchy at best :-)

There're several questions that need to be answered first in order to provide helpful advice: what kind of soil are you growing these plants in? Does the bucket have adequate drainage holes? How many hours is "plenty" of sunlight? Have you fertilized? If so, with what and how often? How do you water, and the frequency?

Even without these answers, I'd venture to suggest that the primary reason the peppers are not growing is because it's still too cold for them. These are very temperature-sensitive plants and if both the soil and air temps are not sufficiently high, they will sit there and do nothing. If this goes on for too long or they are exposed to temps much below 40F, they could die. For optimum growth, they need a soil temperature of around 60F and air temps of 70-80F during the day and 60-70F at night. These temps are just not common in most of the US in early April :-) Growing them in a greenhouse or indoors (quite a bit more difficult) can get around that.

The cabbage is a cool season crop and should grow well in cooler temperatures. But I'd suspect there are other factors limiting its growth that would become clear once the previous questions are answered.

FWIW, there is a Container Gardening forum here on GW that you might find helpful. There's a bit more to successfully growing plants in a container than you might think if you've not done it before.