Is there's any specific benefit to nursing instead of just pumping and feeding from the bottle? Is there anything intrinsic in the act of nursing that improves baby's health or increases the nutrition? Does the mechanical act of sucking at the breast perhaps get at more /different/better parts of the breast than a pump and therefore get more diverse milk? Or does that not really make much of a difference? Can baby get the same benefits from pumped milk?
Nutritionally, there is no difference in the amount of calories or in the breast milk itself.
However, the act of nursing requires a baby to use more muscles than are used in sucking a bottle. This means that babies will only drink as much breast milk as needed; whereas bottle fed babies will develop a habit of overeating.
Additionally, you touched on foremilk/ hindmilk. The first milk during the let down is more liquid and is designed to "quench thirst." The later milk is creamier in texture because of the higher fat content. However, if you give your baby the appropriate amount of milk (2-8 oz depending on age) it doesn't matter that the fore and hind milk is essentially mixed in the bottle.
On a peripheral note: feeding breast milk through a bottle means that the mother must pump regularly to keep up supply. Generally you must pump at the same time as the baby would nurse. You may need to pump longer or more often at the beginning to get used to the pump. Although this doesn't directly affect the question regarding nutritional level, it's important to note that using a bottle to feed breast milk may cause the mother's supply to dry more quickly. Pumping doesn't empty the breast as quickly or as efficiently as a baby (especially once the baby has learned how to nurse). Newborn babies are slow, but once they are a few weeks old, they can nurse in 5-10 minutes what may take 30 minutes to pump.
Personally I nursed my oldest 15 months, and am still nursing my 12 month old. I could not have pumped and given breast milk so long.
I'm surprised this hasn't been mentioned! While there is no difference in health benefits between bottled breast milk and nursed breast milk in the case of a single feeding, there would be a significant difference if nursing were ended completely and a pump and bottle came between mother and child 100% of the time.
The nipple is bidirectional. We think of it as an output, but it is also an input. The mother receives pathogens through the nipple from the baby's mouth very similar to kissing. The mother's more advanced immune system responds and the milk delivers this back to the baby.
This can still work as long as nursing happens regularly in addition to pumping. Our pediatrician suggested to try for nursing once daily. But at least every other day. More, of course, gives a better chance of  the pathogen getting passed and  the antibodies/leukocytes/etc. doing their job before illness can set in.
The milk is the same whether fed directly from the breast or from a bottle. As long as you don't store it more than a few hours, there is no difference.
Then it's just a matter of preference for you and the baby. If you feel giving the breast is a more affectionate way of feeding baby and your newborn likes it, it's fine. My daughter couldn't eat from the breast because of the speed and quantity. From the first few days she was fed pumped milk and she refused to take the breast.
The advantage of bottle feeding is that the father can help from the very beginning and, during the following months, baby will not need a period of adaptation from breast to bottle and mother to father.
No, there is a difference between bottle feeding and direct nursing. Recently I read an article about it. Accordingly it says, antibodies are produced in breast milk as per baby's environment, like saliva and germs. When you pump, only that environment's antibodies are present. When you nurse you would get antibodies of the present exposure. And the act of nursing in baby requires different jaw movements which gives proper structure in facial development further leading to better speech and development, whereas bottle feeding means they are overfed which may lead to obesity...
But in cases if you are working or due to any health conditions you can't nurse... bottle breast milk is always better than formula milk... Something is better than nothing. When there is chance, go for it. What you give now, will give immunity for your sweetheart.
Other than maybe a physical bond, touching, there should be no difference as repecmps mentioned. The milk is still the same, and I have seen plenty of mothers, including my wife, store the milk and feed it later. The sucking motion, as long as you use one of those nipple tops that simulate a breast, should be the same - and even with an older style nipple top there should not be much difference.