Ive played just about every conceivable tune in trios and most times drums and bass were louder than singer and tight.. Having a strong punchy bass tone, and a top notch lead singer/musician tends to be the best bet. Dont try to be like the recording.. Keep the primary hooks then think about space. As long as your tight, in tune with a powerful singer, all will be good.
Two peculiar examples. Ive played 'Forget Me Knots' and 'I Will Survive' with just guitar and drums and the floor was heaving and I seem to remember being very loud on both counts!