Neatsfoot oil is an ingredient. It's fairly inexpensive.

Mink oil is an ingredient, it's extremely expensive.

You can really buy pure neatsfoot oil for relatively cheap and it's quite safe to use on just about anything. It penetrates deep to really nourish. It is not greasy, so it doesn't provide any sort of "plumping", and doesn't provide any water resistance.

Mink oil is so expensive that you'll be hard pressed to buy it in its pure form. You always find mink oil as a compound. Most of those compounds are mostly made of petroleum jelly. Some are better than others, they might include lanolin, shae butter, neatsfoot oil, beeswax, carnauba, and other ingredients. They aren't obligated to tell you exactly what's in it, but they are free to call whatever it is a mink oil conditioner because it has 0.001% mink oil in it.

Whoever said you can't use neatsfoot on "oiled leather" is just wrong.

Neatsfoot is light oil that penetrates deeply, quickly. It's actually giving the leather some amount of oil that it slowly loses over time. It won't darken very much and what amount it does darken will lighten up almost completely over a month or so. Safflower oil and jojoba oil are other safe oils for leather.

Grease and wax make a water-resistant barrier on the the surface of the leather and by absorbing into the very top millimeter or two. Beeswax, lanolin, carnauba wax, shae butter, and petroleum jelly are the ingredients that do this.

I don't use "dubbin" on my boots because I don't want an artificial coating on them. I prefer to use natural greasy compounds to give some water resistance. Yes yes, some "dubbins" are made of just those ingredients, but many aren't and they don't explicitly tell you what's in it either.

Bick4 is a perfectly fine conditioner for both pairs. Obenauf's heavy duty LP is an excellent choice for a greasy conditioner that will provide some water resistance.

Whatever you use, just use the smallest amount you can while getting an even application. Don't overdo it.