The Bren is going to be better for an army on the move, it's lighter, easier to carry ammo for, less prone to getting dirt in the mechanism and therefore more reliable despite the sort of abuse it's going to get in a war. You can also fire it on the move or from a standing position, not something that's advisable with an Mg42
So if you are on the attack and trying to be mobile the Bren is a nicer choice. If you are holding a position and not going anywhere try a Vickers
But if you have to do both and you are in a position where you need more mobility than a Vickers but more rate of fire than a Bren then the MG42 is a good balance, it has the advantages of both but also the disadvantages of both.
To see why you just need to look at how a rifle squad was armed in the 1930s. Germany still gave its guys the Kar 98, a powerful and accurate weapon but slow to load, slow to aim and with a small magazine. You are going to manage at best one shot every four or five seconds, less if you are aiming carefully and someone is shooting at you, and you need to reload frequently. On the other hand a British section has the Lee Enfield with double the magazine capacity, a much easier bolt to cycle, and the advantage of not having to break aim every time you cycle the bolt. A good rifleman could match a semi auto for rate of fire, and aimed fire at that. A British section is going to put ten aimed shots downrange for every two shots the Germans can fire back. Not good if you are German.
This basically means that when it comes to suppression that British squad is going to do a pretty good job based on rifle fire alone, it can put a solid amount of lead downrange, multiple rounds per second for a respectable amount of time thanks to their magazine size, and each round will be reasonably well aimed. The German squad can do none of that, instead it has to bring along its own machine gun. Whereas the Bren is support for the rifles, in the German squad the rifles are support for the MG. Becomes a doctrine thing where the German squad relies on the MG to do the job and the British squad prefers to put more trust in the rifles.
Both have pluses and minuses, the MG can put out a lot more bullets but you are putting all your eggs in one basket. Lose the MG to a sniper, grenade or bit of well placed smoke and your squad becomes largely useless at range. Lose a Bren and your Enfields can still do a decent job of putting down some suppressing fire, at least by 1930s standards. Also much harder to suppress several men with decent weapons than it is to suppress one guy with an excellent gun.
So the Bren fills a role in British squads that doesn't exist in a German squad, and likewise the MG34 fills a role that isn't necessary in British squads where its negatives are considered more important than its positives. The British army of the 1930s was based on a doctrine of mobility, it had a greater mechanisation than the German army managed and being able to pack up and go somewhere quick was considered an important advantage. A Bren fits that doctrine better than an MG34 would and suits the more mobile style of war Britain favoured in the 30s