Draw. At least in the short/medium term
Neither opponent can really get at the other. By mid 1942 the UK was invulnerable to invasion (it had been close to that from the moment Fighter Command won the BoB, once a division of U.S. troops along with divisional sized Canadian troop formations, with full TOE were in place the "close" vanished). The Combined Reich/Soviet navy present nothing but a serious long term irritation (once Henry Kaiser's yards hit stride the KM/Soviet submarine fleets can sink tonnage as fast as U.S. yards can crank it out). The U.S., of course, has two rather sizable oceans as insulation from attack on the CONUS.
The counterpoint is that the U.S./Commonwealth Alliance (even assuming that pretty much the rest of Western Hemisphere joins in) doesn't have a chance in Hell of getting ashore in France, engaging, and defeating a combined Reich/Soviet force, not before the Continental powers acquire the Bomb (assuming the Soviet penetration of Tube Alloys ---> Manhattan is as successful as IOTL). With the Germans involved in a program that, far from "knowing" will fail to one that they know will succeed (again assuming the Soviets share their Intel, which is far from a certainty), it is possible that the "Continental" program may show results more quickly than the Soviet 1949 first test.
As far as the WAllies simply blowing the pougies out of Germany once the Bomb is available, it isn't that simple. First this idea assumes that the Reich would fold after a couple cities got blasted, this is clearly not a established fact, it requires Hitler to 1) give a damn about the average German and 2) act rationally, neither of these requirements stand close examination based on the actual historic record. Next, it requires the WAllies to have achieved the sort of air superiority that was achieved over Japan, another scenario that never occurred IOTL, even with the Reich in its death throes, the Luftwaffe defended the skies, both with fighters and with radar directed guns up to 12.8cm caliber. The early A-Bomb deliver methods required pretty much zero opposition to unescorted small flight of bombers (in the case of Hiroshima the authorities actually sounded the "All Clear" after and earlier raid warning since it was only three B-29s at high altitude, clearly not a threat. Try that over Berlin and, even at 30,000 feet, there are going to enemy fighter on the way into the target and 12.8cm radar directed guns tossing shells directly into the formation's path. Simply not going to work.
The "good news" as these thing go, is that there is ZERO chance of the Nazis and Soviets doing more than tolerating each other for a few years. The Nazis will still see Communist = Jewish conspiracy and be driven to wipe them out root and branch. The Soviets will still see the Reich as a clear and present danger to the Revolution (which, oddly enough, Stalin still actually believed in) and now THE impediment to bringing all of Europe into the "Socialist" Light of Day (i.e. Soviet dominated communist). Give it until mid-1943 when Berlin and Moscow are no longer engaging in anything noteworthy on the ground and the marriage of convenience is going to turn into the Divorce of the Millennia with the WAllies sort of sitting on the sidelines and trying not get anything on their shoes. Once the Germans and Soviets have started their Götterdänmerung and have pulled sufficient forced into the East in their Battle Royale, then the Wallies could conceivably make a Channel Crossing to clear France and Low Countries, along with actions as far as Norway, and if the Reich is getting it's ass kicked badly enough, Denmark.
Once that happens it's time to pull up a couple chairs and make S'mores until they have beaten each other more or less to death then roll in and administer the coup de grace to both of the bastards.
en.wikipedia.org
