Most levers have a tubular magazine which limits the type of projectile you can use. Using spitzer in a tube magazine risks detonation of the rounds in the tube.
The BLR lever has a detachable box magazine so the projectile choices are more numerous.
Although Brownings are very good, a lever will never have he same lock up as a bolt action rifle and this compromises their consitency and accuracy. The 270 is also a long bugger and the throw of the lever is quite long to cycle the rifle. I can't imagine the speed would be much greater compared to a slick Mauser action. Shooting prone or off a bench with a lever is, well, interesting. My choice for a BLR would be a 308, or a 243 if you like velocity. Both these rounds are very similar to the 30-06/270 family in terms of performance and they tend to be more plentiful here in Oz.
In a box magazine lever like the BLR it is easier to determine the condition of the rifle compared to a tube magazine lever. It therefore intrinsically safer than a tube magazine lever. With a tube magazine rifle, extra vigilance is required to make it safe. You can't tell how many are up the tube and the lever has to be cycled a number of times (and then again) to be sure it is clear.
With a detachable box one only has to drop the mag, cycle the lever and the rifle is clear. In most bolt rifles, like your weatherby, you can drop the floor plate, cycle the bolt and bobs your uncle - its clear and okay to put away.
