Beetle should win. Jaime's normal power level is actually a bit below what he could do because he's focusing on less-lethal options instead of the lethal it was designed for, letting the Scarab use it's full arsenal will let it be more dangerous than normal.
Because the Scarab is a weapon designed to take on GL corp members and even though we don't know the exact options that were being formulated, the Scarab was giving him escalating plans of assault against the Spectre that were reaching what was described as "real WMD stuff".
My knowledge on War Machine is honestly a little rusty, so what lets him really stand a chance against a No holds bar Blue Beetle?
Yeah, Jamie was turning down options that could bust continents, which is more firepower than War Machine can output, by quite a bit.
One thing about Jamie's armor: It adapts to his enemy. So, if War Machine can be taken down by, say, an emp pulse, the armor can create one. It was adapting weapons that could hurt Supergirl, for one example.
It even adapted a way to keep Black Beetle from time jumping.