In the Fall of Gondolin [BolTs 2] you may come across a different version of Balrog who are not as powerful and are more numerous and who do die without taking out their opponent. Even Men can kill them. Otherwise they are Maiar who're extremely powerful and so dangerous a foe that if they did not beat you, you did not beat them either. It'd end in a draw, like with Ecthelion, & Glorfindel of Gondolin, and Gandalf. Gandalf himself told the company in Moria, "This is a foe beyond any of you." [The Bridge of Khazad-Dum] The interesting part of Gandalf's encounter with the Balrog is that I generally get the sense that they are hulking figures who overpower you physically, but there is more to them than overwhelming physical prowess. When Gimli and Legolas see the Balrog they are so frightened that they cannot even wield their weapons. There is also his use of magic against Gandalf.
It laid hold of the iron ring, and then it perceived me and my
spell... The counter-spell was terrible. It nearly broke me. For an
instant the door left my control and began to open! [The Bridge of Khazad-Dum]
Gandalf goes over his encounter with the Balrog to Aragorn, Legolas, and Gimli and you see how great a foe this guy is. Gandalf claimed that if anyone saw them fighting on the mountain from afar,
thought that the mountain was crowned with storm. Thunder they heard,
and lightning, they said, smote upon Celebdil, and leaped back broken
into tongues of fire... A great smoke rose about us, vapour and steam.
Ice fell like rain. [The White Rider]
Lightning and fire beating upon each opponent back and forth on Celebdil. It was like a storm their wild encounter. The Balrog was also "stronger than a strangling snake" and tough as well as Gandalf "hewed him". At this point the Balrog had been at a disadvantage because they had fell into a pool that was ice cold and his fires went out. Gandalf apparently still had his sword, the Balrog's had broken. I do not know if he had another weapon to wield. It seems he fought Gandalf with his bare hands while Gandalf still had Glamdring. Eventually the Balrog took off and when his fires came back into play they took each other out.