It can be hard to generalize because the nuances vary depending on a given adjective; it's very context sensitive. A few generalizations:
As VCH250 mentions, when an adjective can express either a temporary or a more permanent state, the short form is used for the temporary state (think "short time, short adjective"):
Вчера она была больна. -She was ill yesterday.
Он больной. -He's sickly/an invalid/has some long-term health issue.
Short forms are often used when there's some limitation in the context; the corresponding long form would indicate a more general, inherent quality. This touches on your example Моя душа полна тобой - my soul is full with/because of you.
Она права. -She's right (about this particular thing).
Наше дело правое. -Our cause is just (an inherent quality).
Он ей не был симпатичен. -He wasn't attractive to her (maybe others did find him attractive, but she didn't)
Он очень симпатичный. -He's very nice/attractive.
Они не способны выполнять свои обязанности. -They aren't capable of fulfilling their obligations. (maybe they can do other things, but not this)
Я его давно знаю, он очень способный. -I've know him a long time, he's very capable (in general).
Short forms are often used with a preposition for phrases best learned as vocabulary:
готов к "ready for," похож на "similar to," знаком с "acquainted with," согласен с "in agreement with," etc.
Short forms can be used to describe an action:
Пить вредно. -Drinking is bad for you.
If none of the above applies to a given context, then the short form, as others have mentioned, often sounds more formal, archaic, or bookish.
Это хороший вопрос. -That's a good question. (normal, conversational tone)
Вопрос хорош. -The question is a good one. (heard in a radio interview with an academically oriented expert)
Learners should avoid using short forms before a noun, since they're only used in the predicate (the English translation will have 'was,' 'is/are,' or 'will be'). Russians can play with word order - in Евгений Онегин Pushkin wrote "Но вреден север для меня." - but note that it means not 'the harmful north,' rather 'the north is harmful for me (doesn't agree with me).'