I will admit the one thing that I realy like Rem-oil for is the outside finish of blued and polymer framed/stocks. It leaves them looking great...just spray a little bit on a rag and wipe it down...it makes them look as good as new. Just don't use too much, because it will 'sweat' off over time.
My old Remmington 522 Viper which I had not shot for ~5 years from the time when I was 17-22 was last cleaned and given a little coat of Remoil when I was 17. When I picked the rifle up at my parents a couple of years ago it had no rust or corrosion and was in really great shape. This was prior to me finding CLP in the Army...and still I use remoil on the outside surfaces because I like what it does and it does not leave an oily film.
So basically when I clean I use Remoil on the outside. CLP in the barrel. A very light coating of remoil in the trigger assembly. Remoil as a coating on the outside of the slide and the outside of the barrel. The rails will get a dab of CLP, and depending on any bad areas they'll get CLP.
In the military it it entirely different...we usually store the weapons dry or with an extremely light coat of CLP since the arm vaults are climate contolled. We don't leave a lot of CLP on the weapons since they don't appear as cleaned when they are inspected...and they will often be dirty from the C in CLP when they are removed from their racks.
We also do a lot of things that wouldn't normally be done to personally owned firearms. We bathe the 'guns' (M240, M249) with carb or brake cleaner and then use hot water on them. This is followed by WD40 to displace the water.
Many of us bring cordless dremels into the field and use that to clean bolts. It really makes quick work of the bolts on the M4/M16's.
Then wthen it comes time to actually throw lead downrange, we apply CLP pretty liberal on the bolts of the M4/M16s and coat the inside of the 'guns' pretty heavy. CLP does stay in place pretty good when burning through a couple thousand rounds at a time
The one problem with CLP and the Army is that it is used as a catchall. I think the LP portions are GREAT, but the cleaning is extremely slow. Hoppes No9 works much better to remove carbon...but then again CLP from an infantry mans standpoint is pretty nice for the simple fact that there is only one little bottle for me to carry with me.