The BAR was the current-day Squad Automatic Weapon for the U.S. military. As a SAW it was totally outmatched by the MG 34 and MG 42. It wasn't belt-fed and didn't have quick change barrels so in combat the volume of fire it could deliver was nowhere near what the SAW of a German squad could put out. The comment about 'BARs outflanking and outmaneuvering MG 42s' either has to be talking about MG 42s configured as a 'HMG' (tripod, telescopic sight for sustained long range enfilade firing, etc.) or it's propoganda. The Germans wrote the book on infantry tactical doctrine, fire and maneuver, etc. from the later days of WW1 thru the entirety of WW2.
The M1 Garand was by far the best standard issue rifle of WW2. You can't count the StG 44 in the competition because it wasn't near standard issue. In a CQC situation you'd have a huge advantage if you had a semiautomatic M1 Garand and your opponent had a bolt-action rifle. Also 8 or 10 guys with M1 Garands that knew how to shoot and were aggressive enough to shoot (this was actually a problem sometimes for the U.S. Army in NWE during the last year of WW2 due to the high % of inexperienced infantry replacements going 'into the line' and the lack of experienced battlefield NCOs and Officers) are going to generate a much greater volume of fire than an equivalent # of bolt-action rifle armed soldiers. The Germans picked up M1 Garands whenever they got the chance as long as usage of the weapons was feasible from an ammunition availability standpoint. Fortunately for U.S. soldiers the only time this was really an option was during the 'Battle of the Bulge' but during that 'battle' there were a lot of German soldiers using M1 Garands as ammunition and Garands were easy to accquire. I think the main reason they didn't use captured American M2 .50 HMGs was a lack of available ammunition. They used captured Russian 12.7mm HMGs on the Eastern Front I'm guessing it was easier to get ahold of ammunition for them.
There's lots of pictures taken during the 'Battle of the Bulge' where you have groups of Germans that have either a German or an American automatic or semiautomatic weapon. It isn't uncommon to see photographs of German soldiers also not issued a pistol carrying M1911s during the 'Battle of the Bulge' (and on the Eastern Front nearly every German soldier carried some type of captured pistol). As far as German use of captured American weapons in general I think ammunition availability was the primary consideration. I don't think ammunition incompatability would have kept the Germans from using an American rifle when their SAWs were German. From the top down 2 SAWs was standard for the Germans by the 2nd half of WW2 so MG belts were easily available at the squad level. And if you are having to take individual rifle rounds from your Kar 98k to 'belt up' for your SAW gunners - things are almost 'over' anyways. I think the battle issue for German riflemen was something like 100 rounds on the rifleman and another 100 rounds per rifleman with the company ammunition train. Your SAW gunners would burn through that very quickly if you were down to issued rifle ammunition alone.
The Germans also really liked the Soviet PPSh-41 SMG. In the latter half of WW2 it was close to standard issue on the Eastern Front due to the large volume of weapons and ammunition that had been captured. The odd thing is that German reconaissance units heavily favored the PPSh-41 SMG, and Russian reconaissance units heavily favored the MP-40 SMG. I think that might have something to do with doctrine - German reconaissance units were used in an offensive role far more often than most other Nations reconaissance units. The PPSh-41 SMG was superior in terms of volume of fire due to having a large drum magazine. The MP-40 SMG was far lighter, and the Russians used their reconaissance units in 'LRRP' style operations far more than anyone else during WW2.
I haven't shot an M1 Garand (yet). But a high % of the U.S. military snipers that I know fairly well have match M1 Garands with a scope at home. They think very highly of that weapon.
I have fired the M14 a great deal. Can someone who has fired both weapons tell me how this compares to the M1 Garand? I recall hearing that the M14 was heavily based on the M1 Garand.
They went with 3RB on the general issue -16s because the volume of fire isn't much reduced from a fully automatic -16 when you consider you only have 30 rounds in the magazine to start with.
Any modern battle/assault rifle is difficult to hit with when firing 'full auto' unless you are using short bursts or you are firing at short range. If you are firing in short bursts already...3RB is basically the same thing. Even with a fully automatic M4 most of the time you are using it as a semiautomatic weapon. If you know what you are doing a semiautomatic M4 can get the job done in 99% of the situations you are likely to face as a non-auto weapons guy. Auto weapons guys have different responsibilities and need the big barrel and the belted rounds to compensate for their tiny weeeeeee-eeeer I mean do their job.

Schadenfreude has it right - in an unrestricted land warfare situation (i.e. not CQC, etc.) your auto weapons guys are your killers (and they never let anyone forget it ehehehe). During some training a couple of years ago there was a platoon that had almost double the normal # of auto weapons - out of 17 guys they had 6 M60E3s (the whining from the guys in that platoon that weren't commo guys - and thus had to carry belts for the 60 gunners - was whining the likes of which I have not heard since). So you have several platoons training in the same area over a several-day period. At night, you always knew if it was them or one of the other 'normal' platoons that was popping an ambush on the instructors.
Mike/wulfie