www.bjmp.org/content/clinical-audit-babies-admitted-paediatrics-unit-crosshouse-hospital-within-7-days-birth
Out of 50 babies readmitted in the first week of life, 29 were due to weight loss, poor feeding etc. 90% of these were breastfed
Patterns of maternity care in English NHS trusts 2013/14 - RCOG (of doc) states that 3% of babies were readmitted within 28 days of birth.
Obviously there is a difference in the time period between these two sources but if (and I appreciate it is a bug if) the reasons for admission in the first week are about the same as the first 28 days then that equates to 1.74% of babies being readmitted because of poor feeding. 1.57% would have been breastfed and 0.17% bottle fed.
So bottle feeding has a higher risk of admission for ear infections and gastroenteritis but a lower risk of feeding issues, excessive weight loss etc.
Breastfeeding has a lower risk of admission for ear infections and gastroenteritis but a much higher readmission rate for feeding issues, excessive weight loss.
In both situations if we are being a bit pedantic about it, we could say it's not the method of feeding but how it is administered /lack of support causing the issues (insufficient intake of milk or prep of bottles).
In both, in most cases the babies recover well enough. Looking only at dehydration where it is very severe, looking at organ damage etc is not comparable with a tummy bug unless again we are only considering the worst tummy bugs, where the babies life is on the line. For most ear infections, or tummy bugs, the baby will be fine, equally most babies with feeding issues will be fine.
But it seems that overall a baby has a similar chance of readmission whether bottle or formula fed, just for different things.
So maybe we shouldn't insist that one method of feeding is better, and instead encourage parents to feed their babies in whichever way they want to, without trying to persuade them one way or another, and without judgement.