I just did an experiment. What I found was that the FTDI with DIY auto reset circuit does not work on both an ATmega16U2 and a CH340 based "Uno" style board, no matter if I'm using DTR or RTS. I used the same DIY auto-reset circuit on a Pro Mini (which doesn't have an on-board USB to TTL serial chip) and I was able to upload using either DTR or RTS. The Pro Mini is an ATmega328P on which I have installed the Uno bootloader so the only difference from the other boards is the lack of the USB chip.
This tells me that the on-board USB to TTL serial chip somehow interferes with the working of the DIY auto reset circuit. So my suspicion is that it was purely by chance that DTR works for you. If you end up starting to have problems with your DTR-based system, or you decide you want to give the RTS one another try, I would suggest cutting the RST-EN solder jumper on your Uno. That will disconnect the auto-reset circuit of the on-board USB chip and prevent it from interfering with the DIY auto reset. After that, I would expect RTS to work for you.