Well, considering that there is no preparation and that neither of them have their typical equipment, I think Barry would have a slight advantage, after all he is more impressive in terms of skill. A bloodthirsty Barry was able to clear out a Monastery full of various heavily armed gangs (one of them efficiently trained by himself), just by being angry, achieving it with only a gun in hand. He was also able to contain and defeat Ronny, who would probably be one of the best Taekwondo fighters on Earth, winning by wearing him down with a blow that would break his trachea and eventually leave him tired. In terms of stealth, both seem to be more or less comparable, after all Butcher was also a military man and has led covert operations, although I tend to think that Barry is more skilled, as something not mentioned in his profile is that he was able to escape from a prison, which was on high alert but still managed to escape successfully without leaving any traces of where he was going, with the police only able to speculate on his whereabouts and never finding him.
It is also worth noting that Barry has an edge in LS, being Peak Human and possibly taller as well as having higher Durability/AP, as when he is bloodthirsty he has a stat boost, which should be substantial. The only stat that I am sure Butcher would excel in, could be endurance, as he has shown the ability to withstand attacks from those much stronger than him and still recover.
