Hale Pet Doors and Security Boss pet door makes some of the best pet doors available. The last one I had was double pane with e-glass and custom fit to my door. Having said that, I recently had a door installed through the wall and we love it. We have a poured wall home, and it took the guy about 4 hours to cut through, but it look fantastic and works great! Our entire back yard is screened in, so no worries about other animals using it. Our 2 cats use it all the time.
When you install a pet door in a sliding door, the main door only slides part way open. In our case, it made the door unusable. There are companies that will install one in the actual sliding door - they replace the entire pane of glass with a pet door in one corner. The issue I was with this was:
1) It's very expensive (around $1,000)
2) If the window leaks, loses a seal, or gets broken, you have to buy an entire new custom window (see #1)
3) The through the wall install was about 1/2 of the price of this option... and it works great and leaves the slider alone.
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