Regarding IE, the resize issue occurs because, the re-sizing is done by CSS resize
property, which is not supported by IE.
This issue can be solved by using Resizable plugin:
Example
HTML:
<textarea type="textarea" id="txtArea" placeholder="enter the message..."></textarea>
jQuery:
$("#txtArea").resizable();
CSS:
#txtArea { overflow: hidden; /* for the scrollbars */}
And when it comes to Firefox, it always adds an extra line after the textfield. If you want it to have a constant height, you need to use CSS.
So overall there is no out-of-the-box solution, when it comes to the height or any other styles of the textarea in different browsers. So only possible solution left would be to use CSS or Javascript.
If you want to target Firefox:
@-moz-document url-prefix() {
textarea {
height: 4em /* or use px to be sure */ ;
}
}