I use a lot of both!
There are all these long debates on oils versus greases and they can get very heated. Greases are a thickener with oil. The oil does the lubrication, the thickener does important things beside making the compound semi solid. Greases and oils have additives that make a huge difference in what the grease or oil does. Some additives make the grease or oil great at rust resistance, but not so great as a lubricant.
The primary reason we use greases is because the stuff sticks to surfaces. This should be a Captain Obvious moment, but think about it, grease clings to stuff and will leave a thicker layer on the surface than an oil. Sometimes that is just great, sometimes it is not.
For firearms the lubrication requirements are not that severe. Can’t say how many times I have seen bone dry firearms banging away at the range. A couple of times I remember semi auto pistols not cycling properly until they received a squirt of oil on the rails and locking recesses. Bullseye pistol shooters lube so much, that they told me the elbow was the drip point!
I use Mobil 1 synthetic a lot. I prefer oils in semi automatic pistols because I found greases got into corners and was hard to wipe out. I use a combination of light greases and oils in bolt rifles and semi auto rifles. I often paint the bolt lugs with Lubriplate 105, a very thin grease, and I oil everything else. I paint grease on with a ¼” flat artist brush.
http://www.lubriplate.com/Products/.../Lubriplate-No-105-Motor-Assembly-Grease.aspx
I bought a couple of quarts of LSA
http://www.e-sarcoinc.com/lsalubricant1quart.aspx
and use that when I am bored. I think LSA is a great idea for a semi auto pistol as it is a little thicker than an oil, it is a semi fluid, and it wipes out easily.
If I have any lubrication advice for Garand and M1a shooters it is : LSA in the winter and Lubriplate 130 in the summer.
http://www.lubriplate.com/Products/Multi-Purpose-Greases/100-130-Series.aspx
But more important than choice of lube, is to keep it lubed!