I'm assuming you mean [water-soluble] latex-based vs. oil-based paint. Can you even use oil-based paint for painting your house anymore? For some reason I thought that was against housing code for environmental reasons.
I would use latex paint. Pick a nice glossy white for the trim.
I've used this Benjamin Moore before. You have to work quickly with it, but it can look really good.
Latex paint is easier to work with, dries very fast, water cleanup, and has no fumes. It is the best choice for DIY. If you are hiring a painter or feel up to it yourself, I would consider oil because it is more durable over time. One other thing to consider is oil based paints can be sanded down in the future if need be, sanding latex paint is frustrating and no fun at all - turns to bubble gum consistency under heat from friction.