the image filesize is too big.

Change the settings in your php.ini or .htaccess to allow for larger files to be uploaded.

Yes. I do understand the issue.

We should be showing an user friendly error message "Image size too high" instead of throwning a fatal error like above. Does that make sense?

"Fatal error: Allowed memory.."
-- reported by PHP long before Elgg code gets control ;-)
~> 'we' @error = 'PHP'

Sad to hear that. Hope there is some fix instead of chaing the size in config.

'config' ? u mean php.ini !
'fix' ? where ? in php ??
try -- http://php.net/manual/en/function.set-error-handler.php
there *is a way out ;)
you code - i will test

Tidypics has complicated code that tries to predict how much memory the resize operation is going to take and displays an error message if it thinks it is going to crash. It's still not a guarantee.

Switching to command line ImageMagick fixes this.

My host has a 10s script timeout, wsd (php fatal error) when user tried to upload an avatar that exceeded this. This fixed it for me:

register_shutdown_function('shutdownFunction');
function shutDownFunction() {
    $error = error_get_last();
    if ($error['type'] == 1) {
        register_error(elgg_echo('avatar:upload:timeout'));
        forward(REFERER);
    }
}