I asked the same question to the manager of the local Leather Factory. He replied that the Alcohol-based dye sits on top of the leather, whereas the Oil-based dye penetrates the leather. He said that in the long-run the oil based dye was better for the life of the leather.
Plain and simple Bull!
(of course he's going to tell you that since the oil dyes are about twice as expensive!) - I use the spirit dyes (Fiebings or Lincoln) exclusively when not using natural dyes - but I have used the oil dyes. The way to get penetration is to properly deglaze the surface and then dampen it with water - the water will open the pores and allow the dye to penetrate. Actually you do it in one step - use a spray bottle of 70% Isopropyl alcohol and spray the surface until well dampened. The alcohol will deglaze it in all but the most difficult cases and the 30% water will dampen it. After dying and when totally dry and the color you want - the next step is to buff off the film left on the surface - this is EXTREMELY important since if that powder is left on the dye will rub off. After that add a LIGHT coat or two of a light leather oil such as Lexol Conditioner. I don't like the oil mixed with the dye or before dying because the oil will act as a carrier for the dye and will cause bleeding unless completely sealed, which can be a nightmare, especially with black dye. Oiling AFTER the dye will help immensely in this respect, especially on the flesh side.
If you really want to use oil dyes though the are easy to make yourself - just add oil to the dye. To do it properly you will need a food blender (not the one from the kitchen!) some light oil, I use cheap olive oil, some Lecithin capsules, and regular spirit dye. Mix a pint of dye with two or three Lecithin caps (squeeze the liquid out of them) and the oil - start with a couple of tablespoons and add more until you get what you want, generally no more than an 1/8 of a cup to a pint of dye, keep whirring it until mixed and then whirr it up before each use. I learned that from an old saddle maker back int he 1960's, only he used an egg beater - well actually I used the beater - apprentice = slave
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The commercial oil dyes are in fact basically a similar mix - look at the ingredients some time.......unless they've changed the ingredients in the last few years oil dye has all the same dryers/thinners such as toluene as the spirit dyes do.