Should You Leave or Stay?
This question has plagued many mortal souls. Let's look at your two assertions. You say if you stay it means feeling alone, but if you go you will actually be alone. The funny thing about these two options are that they are both presumptive of a whole myriad of unchanging conditions. Reality is constantly changing and the future is therefore a liquid unknown, rather than a solid platform upon which we stand.
It is sink or swim my dear and swim you must, lonely or not...so let's look again. Lonely feelings like other feelings come and go and depend on so many internal and external factors. Actually physically being alone is almost impossible, since we live in a world of billions of people and you are not in solitary confinement.
So, dramatics aside, this "being alone" really means being physically distant from this one person that you do not feel a closeness to presently. If you remove yourself physically from this person there is a chance that your own feelings for him/her would increase or decrease. There is a possibility that this person could then chase you for awhile or let you go, but it is a risk.
Feeling lonely in the midst of a relationship is fine sometimes, but not always. Another person cannot conquer your moods and blues. No one can do that for you. So, yes it is okay to have some times of lonely solitude and private contemplation. If your longing for closeness will never match your love interest's desire for closeness with you, then you need to deal with that.
Some people are on opposite ends of the spectrum with their desires for emotional and physical intimacy and will never completely feel in sync. Before separating, it might be worth several discussions on what his/her needs and desires are for closeness and perhaps with patience and communication the two of you will find common ground.
One thing I know for sure... The Clash Rocks, but so does Al Green.