The long answer to this question would concern such factors as lighting, hues and depth high-brow renaissance artifices such as chiaroscuro, contrapposto & sfumato.
The short answer is "YES" or "DEFINITELY" !!!
Take a look at some of our examples below, to see what you think
If you can see the beauty in Oils, you are not alone, the colours, lighting, depth and beauty are staggering, a drawing is always going to be more flat and lack depth and thereby convey less realism. Our brains see in colour and we even dream in colour (not black and white), so to really capture the heart and soul of your favourite pet you need to commission it in oils.
But if you don't have the budget then you can always chose a dog drawing instead.
It's entirely your choice, but oil paintings are better , HINT, HINT!