Bitcoin cant give you all those things which girlfriend can give you all the time. I mean bitcoin is not even physical and you cant attach with it. Its just money and it can be earned at anytime in your life. Just because you got the 10 Bitcoin doesn't mean anything to me. What would you do with it alone?
I mean all these things will matter if you are really in a serious relationship. If you are not in serious mode or whether your girlfriend is cheater then I am sure you should go and grab the 10 bitcoin. Later on find someone who truly deserve your love and live happy life as you have 10 BTC plus love of life. How about that one.
But If you love your Girlfriend more than anything else then there is no doubt that '10 Bitcoin' is nothing because you can still earn 10 Bitcoin or more in your lifespan when you are motivated by the one that you really love. Money can't buy happiness and we all know that, I think you only ask this kind of question because you don't yet experience a real love.