Well, owning a BAR I'm a bit biased, and I've only fired a Bren once so....
Thoughts on the BAR.
Mag is on the bottom. That top feeder reloads pretty quick but you had to either stick your head up to reload or turn the gun on its' side, so there really wound up being no practical advantage when someone was shooting at you.
Reliability of the BAR exceeds the Bren from the reading I have done. There are many accounts from BAR men in WWII stating that they never replaced a single part on their rifle. The only real reliability issues came in the Korean War when many reconditioned WWII BARs were sent out with the old recoil springs, causing some problems for a short time. Early in VietNam there are many stories of SF guys dumping the M16 to get a BAR for the reliability. They were used extensively there early on when the M16 was still having startup problems and then given to the Montangnards who cherished them.
Weight of the Bren in use exceeds the BAR by quite a bit. The BAR bipod was usually the first thing a BAR man threw away. They were rarely used in combat. The majority of the combat photos in the BAR book "Rock in a Hard Place" shows the bipod removed. The posed training photos always show it, but it's usually gone in combat, especially in the paratroops.
Accuracy. The BAR could be fired semi quite accurately by a good BAR man. Though the majority of BARs did not have a semi selector, a trained rifleman could do semi quite well on the slow rate of fire setting. I can get it to work about half the time. When I can, the accuracy is astounding. There are stories from BAR men in the Marines bragging they can "put all 20 rounds in the same hole" with their rifle.
As for the barrel not being field replaceable, that might be a bit of a downside for the BAR but not as much as you'd think. Because the mag only holds 20 rounds, the sustained rate of fire for a BAR is really not enough to melt barrels like a real machine gun.
And that's the last point, the BAR wasn't really deployed as an LMG, the M1919 was the LMG of its' day. The BAR was deployed as a "Squad Automatic Rifle".
The Bren is a fantastic weapon, with 30 years newer design don't forget, but it's not really a direct comparison between the 2 weapons.