This was probably discussed to a certain [large] degree in the previous mega thread about the magic factor in a 'magic' lens.
Yes, equipment does make a difference, but it's not the be-all and end-all. It is not a 'big' factor. Those photos have probably had a good deal of thought gone into the lighting, pose and processing. Not to mention that with subjects like that, any photo would positively 'glow' with appeal, if you get what I mean.
But back to the point. For example, in comparing results from a P&S and a DSLR, all other factors remaining the same, the DSLR (especially if shooting RAW and processing into JPEG), would give a little more depth and smoothness in tones, colors and additional detail compared to a P&S. Clarity is usually better.
In a recent trip to NZ my brother used an S3IS and I used a 1D Classic. He claims that he cannot pull off a photo as nice as mine. Truth be told (and I told him too), the gear makes a difference. In terms of photographic skill we are pretty much on par. He is more creative than I am, but the sheer clarity of a 1D Classic RAW converted to JPEG usually surpasses a JPEG out of an S3IS.
That being said in some shots he beat me to shreds by being able to zoom from 36 to 300mm in an instant and I was still busy changing lenses.
There's a strength in every piece of gear, but you need to know how and when to use it. If you hunt for something that is perfect for every purpose, it may be a long and expensive chase. There's nothing that 'does it all' at this time, although that day will invariably come. Whatever equipment you have, shoot lots with it, learn it inside out, and you'll be able to produce the best possible results from any equipment.
Start off with shooting everything in RAW and then process in Canon's Digital Photo Professional using Picture Styles. I'd be surprised if you say it made NO difference to your photos.