Eb major triad over C major triad: love it, love it

I'm in love with this particular bitonal tension. Here's something interesting. I could easily rearrange the notes in these two triads to make it conform to a C dominant 7 sharp nine (so-called "altered dominant") kind of thing, a very common jazz sound...and yet if I don't try to box it in like that, if I keep envisioning and playing and hearing it as two separate triads sounding simultaneously, the mood and feel is entirely different from altered dominant.

I've been playing with it this way: 'comping simply on the root position triad in my LH while noodling on the opposite triad in my RH, i.e., Eb major "over" C major for a bar, then switch to C major "over" Eb major for a bar, etc etc ad infinitum. It's fun. I highly recommend it.