What to do you think about this parsing: (子どもたちが話している)(にぎやかな声). The verb phrase modifies にぎやかな声 as a whole.
The て form and 連体節 (modifying with a verb phrase) doesn't serve the same purpose. て tends to stream-line (one things after the other) whereas 連体節 modifies the things that follows.
(子どもたちが話していて)(にぎやかな声), the parenthesis can't be placed like that. At most, you can insert a comma : 子どもたちが話していて、にぎやかな声(…) but it doesn't really make sense if you don't complete the … part.
In (あったかくて) (おいしい料理), here again parenthesis can't be like that. あったかくて、おいしい料理 (The food is warm and and it is good/delicious) (another way to understand it would be: The food is warm and (because of that) it is good/delicious)
More information on how to parse sentence can be found in Appendix 8 of the book "A Dictionary of Basic Japanese Grammar".
And if you're brave enough 連体節 are discussed in details here ;) (beware EUC-JP encoding)