Hello,Welcome and thanks for your question. Neither really "dilutes" oil. Cold water should help keep oils from solidifying and sticking to cold metal when they get further down the drain past your sink, helping some to avoid a clog. However, the best idea is not to dispose of cooking oils in the drain at all.
For oils that are solid at room temperature (bacon and other meat fats, butter, margarine) you can use a piece of aluminum foil formed over the drain to make a vessel into which you pour the oil. It will solidify and you can wrap it up and dispose of it in the trash can. Oils that remain liquid at room temperature can be poured into a zip-lock bag and also tossed in the trash.
If you don't have a lot of fat to dispose of, thoroughly mixing it with hot water and lots of dish detergent until it is completely emulsified (i.e. no grease floating on the water) will also help prevent clogs. The down side is that it takes a lot of soap to do this.
Hope this gives you some new ideas to try.
All the best,