This is my take on the topic, drawing on my knowledge of the language. Anyone with superior Japanese language skills, feel free to correct me if I'm in error anywhere here.
Like so many aspects of the Japanese language, "好き" (romaji: suki) can have a modified meaning depending on the situation and context. The most basic definition is "like", such as when referring to things, items, etc.
Example 1:
私はアニメが好きです. = I like anime.
If used in reference to a person, however, it usually has somewhat of a romantic connotation.
Example 2:
私は<person's name>の事が好きです. = I love <person's name>.
"大好き" (romaji: daisuki) is an exaggerated version of "好き" used to emphatically express a liking for something or someone. It can usually be translated as "love".
Example 3:
私はアニメが大好きです. = I love anime.
Example 4:
私は<person's name>の事が大好きです. = I love <person's name>.
While "好き" and "大好き" may be interchangeable in terms of expressing affection for a person, the latter is still a stronger expression. "愛している" (romaji: ai shiteiru) is an even stronger expression of love, but it's only used with regards to people. However, it isn't used all that often in manga or anime. I can only conjecture that it's possibly because it implies some level of truly intimate feeling for a person and we all know how well the Japanese deal with intimacy, especially in public.
