Having stayed both on-property and off-property, it's hard to say that one is particularly better than the other simply because each has advantages/disadvantages that the other doesn't. For on-property, there are some truly great advantages that include (depending on where you stay): fantastic resort theming, incredible views, terrific convenience in location and transportation (i.e. monorail), and of course the feeling of being immersed in the World when you stay onsite even if you're not in a park at the time. Disadvantages of on-property sites (again, depending on where you stay) include: EXORBITANT room rates, some resorts (and their rooms) seem to be little more than a Motel 6 but with more expense put into theming, internal bus systems or stops that cause delays in your travel through the World, noise and obnoxious fellow guests (this primarily when in a resort occupied by cheerleading team there in Disney for their competitions).
Off-property has some advantages in terms of some offering far nicer rooms and amenities for the money you'd be paying (such as complimentary breakfast and shuttles to Disney), also the benefits of you being able to drive anywhere and anytime you want (yes, this applies to on-property places too, but I find that once I get to my resort, I don't want to use my car until its Leaving Day). Disadvantages of off-property include the lack of feeling of being enveloped in the Disney magic (you basically feel like you're on the outside looking in all the time, even if you take the shuttles every day and spend all day in the parks), location and lack of great views, and some of the convenience of Disney transportation such as being able to wake up, dress, and hop on the monorail (or take a boat) and off you go.
Like I said, each has its pros and cons, but certainly if you're cost-conscious that's likely going to be the determining factor. But if you're splitting the costs, my opinion is to stay on-property in a deluxe resort - if you're able.