I agree with Linda, that there can be a subtle difference, with one being a shade negative and the other, a shade more positive. But to my mind, they both imply relinquishing control, and that make one feel rather helpless. So, I would suggest a slightly different outlook again: Acceptance.
In my head, acceptance is not just going with the flow, it is swimming with the flow. Going with the flow implies for me being totally passive, like a limp leaf on the surface of a stream. You go where ever the current takes you, good and bad. But with acceptance, you choose to allow the current of the life situation take you in whatever direction it will, but you have not relinquished control by doing this - you retain the ability to steer left, right, centre, up or down in along the way. For example, it could mean choosing to make the best of an unavoidable bad situation, or even choosing to make the most of a good one. An illustration: Someone who has been driven by circumstances or biology into a seriously bad depression is in an unavoidable situation, but they may choose to look for the humour in the darkness. For example, if you choose to look you will always find something that looks funny, in a black-humour way, or even someone who looks funny, at funerals. You can look to find them or you can keep the eyes low and just cry all the way through the service. A friend of mine died. His name was Steve. He had dedicated his life 100% to animal rights. He lived a poor and vegan lifestyle (not just vegetarian). He helped manage and run an animal rescue centre. In his "spare" time Steve would disrupt fox hunts, he'd hunt down people convicted of animal cruelty and beat them, he raided animal testing laboratories and "liberated" animals in them, etc etc. (I didn't do any of these things! I'm telling you this just so you get an idea of how passionate Steve was about The Cause of animal rights.) Being a vegan, he would not eat or wear anything derived from animals - no leather, no wool, no meat nor eggs or milk, etc.. As his coffin was carried into the chapel I spotted a couple of the pall bearers were wearing leather shoes, which would have aggrieved Steve had he known. Now, this was a desperately sad place to be and something I could not avoid. Nevertheless, I retained some measure of steer .... I imagined Steve waking up from the dead, before he could turn in his grave, busting his head through the top of the coffin, looking at those pall bearers and shouting in his notably foul tongue,
"You ####s!!!" And then to the rest of us, "Get those f####rs away from me!"
I'm not sure if I have explained that very well - I know what I mean but words do so get in the way of communication!
I think it has a lot to do with the circumstances. You cannot alter the past or change the inevitable. You can only deal with the inevitable, which need not be giving up nor surrendering. There is a proverb "He that fights and runs away, may live to fight another day". You have to choose your battles so as to fight those that you can win. This is strategy and is as much a part of life as of battle.