Everybody has their favorites...
But even though they often filled the same roles in combat, design philosophies are very different, as one might expect considering the near quarter century between the designs of the two guns.
The 1919 Browning is just the lightened, air cooled version of the 1917 water cooled gun. There are some minor differences, but basically its the same gun. And like ALL military small arms designed before (and during WWI) they were built like civilian guns in the fact that they were intended to be durable.
WWI changed everyone's thinking about combat, being the first war where the machine gun ruled the battlefield. Heavy built, built to last. The Maxim gun, was the main weapon, and used by both the English and the Germans.
By the closing years of WWI, some lessons had been learned, and the Browning has improved features over the earlier WW I machineguns. But there is only so much that can be done with a design, without making it into a completely different gun. We used the Browning .30 in WWII, and used it A LOT, because it was what we had, and were making.
Germany, on the other hand, as has been said, basically had to start from scratch when they rearmed. And they had a different tactical doctrine than we did. The MG 34 is a masterpiece of design, but it is also made more in the traditional manner than later arms. It was the pressure of wartime production requirements, and some lessons learned that led to the MG 42. Propaganda aside, the Nazi war machine was nearly always on the brink of being critically short of small arms, and used captured weapons, and captured weapons factories extensively to supplement the German produced arms pool.
Note that they contined to build Lugers (p.08) until 1942, when it finally became clear that cost (in terms of skilled labor time) could be better used making other arms. The MG 42 was the first hugely sucessful design that took into account the fact that the battlefield life of small arms is not very long, and its a waste to make them "the old fashioned way".
So, stampings were used for a fair part of the gun. Cheaper in cost, and much cheaper in terms of production time. For us, there was no pressing need to replace or supplement the Browning .30, because when we got going, our production capacity dwarfed all the other combatant nations. Only the Soviet Union came close to matching us in arms, and they were able to do it in some areas only because supplies of materiel from the US (Lend Lease) meant they could concentrate production on arms. The Soviets didn't build as many trucks as they needed (or used), for example because we sent them thousands of Studebakers. The capacity they would have needed to use to build trucks could instead make tanks.
We also had an unsurmountable advantage in that our supplies of raw materials were secure and nobody was bombing our factories.
The Germans built a great gun in the MG 42, but they needed to build a gun like that. The lessons of WWII meant that the Browning .30 was a luxury car, and what modern war needed was an economy car, and lots of them. When we did get around to replacing the Browning .30, we went with a gun that did borrow (or directly copy) many of the features of the MG42. The M60 was better suited for modern war, but it was NOT a better gun than the Browning. In fact as a fine firearm, the m60 was a piece of crap, with many flaws and faults. ITs true we took lots of its design from the MG42, but we didn't do it right. Many of those flaws were eventually corrected, but it took considerable time, and its still "the pig".
All else being equal (and it almost never is) bigger bullets tend to work better.