Without modification (removal of the reflector screen) the CS4 has a narrower forward beam and lower gain (about 2 dB less) when compared to the DB4e. The wider forward beam of the DB4e is the result of the design, four elements stacked vertically. The CS4 forward beam is narrower as the result of the horizontal stack of two dual elements. Removal of the screen of either antenna lowers the forward gain significantly, though I know of no specific documentation of this modification.
If you want to try for bi-directional reception, removal of the reflector is a logical approach. Simply keep the hardware in case you need or want to restore factory designed performance. I simply don't know which antenna will perform best if modified. If anyone has documented either antenna with the reflector screen removed, please share the results in the
Antennas forum. It's asking a lot, but I'd be quite curious to see what happens to the SWR when the reflector screen is removed.
The DB4e is the best antenna of the two if your goal is reliable reception of the UHF signals to the SW & NW. I say 'best', because the beam-width of the DB4e is wide enough to 'see' both groups of stations and the the antenna has additional gain.
So, the points are,
1. You've been offered several valid ideas. Each has it's merit and to say the other is 'wrong' is being overly negative.
2. One thing we all seem to agree on is, outdoor mounting is ideal. That may well be a far more significant factor than a few DB gain or degrees of forward beam-width.