When writing a letter to appeal a college admissions decision, should the letter be concise or long and heartfelt?

It should be concise, professional in style and heartfelt. Your goal is to persuade the reader to re-evaluate their decision.

You want to convey in a factual and professional manner exactly why you feel their decision is flawed, yet you need to also create an emotional bond with the reader to try and build a sense of compassion or connection. The goal is to persuade the reader and that requires a factual presentation that also creates an emotional connection while also maintaining the reader's interest.

It is a fine line to walk, but effectively doing so will not only result in a letter whose contents may sway opinion, but also in a letter that is an example of the excellent quality of work that the write is capable of.

And, as another answer indicates, it is critical to know your audience when attempting to persuade them.

The letter should be concise. The people who read college admission letters
read hundreds and thousands of letters and are very experienced in what they do.
Chances are, by the time they get to your letter, they would already have read
many and are exhausted. Many people write about the same thing: awards they
recieved, sports they played, and etc. What colleges look for is someone who is
mature and unique. They look for a person who is not set on what they want to
be in the future but willing to look into different programs that the college offers.
For example, my tutor went to Columbia University and in his letter, he talked about
his past experience with tennis rackets. He discovered a way to make tennis rackets more appealing to customers and was very successful in making his family
business lucrative.

Try to interest the reader by making your letter concise but unique. Be sure to
contemplate much about what you want to do in the future and then begin writing
your essay. Make yourself sound interested in the college and be natural. Don't
fabricate emotional stories about dead relatives, divorce, or talk about controversial
subjects such as religion or politics because the college admission readers have
read it all. They will know if you are ready for their college.

* one tip, as long as you have a good GPA and a high SAT score, most colleges
won't care if your letter is concise, long or heartfelt. Just make sure you study
and spend your time preciously. This only applies to those who have a very high
GPA (4.0+) and SAT score (1400+).

Depending on your college, most college staff are of a particular political nature - if it is a conservative college, several paragraphs of conciseness and one paragraph of heartfelt is a good ratio. If it is a liberal college, one sentence of conciseness is all that is needed to precede several long, heartfelt, grovelling paragraphs.