Well, BE is using the same engine as Civ V, only they dropped the DirectX 9 support so it will run on anything that Civ V runs in DirectX11 mode in.
Given how many years ago that was when Civ V came out, every new machine sold today will have the hardware support needed for DirectX11 to at least run. If you have other more intensive graphic games you are also thinking about buying, those are actually going to increase what specs you need.
How late game lag compares in BE vs Civ V BNW though is just wild mass guessing. Empires have less penalties to self expansion in BE (and in addition one of the victory conditions requires it), which suggests potential for more lag in BE, but removal of actual trade units and the changes from city states to outputs suggests a lot less lag.
But actually the biggest factor is likely to be a hidden one that we won't know until some of the source code is released to modders at some unknown point post release. If when making BE they took the time to redesign the guts of the game layer, a lot of lag could be removed. But if BE was just clobbered on top of the Civ V code, then that would suggest increased lag.