They are exactly the same, same parts, same everything. Only the looks differs a bit. Onkyo is a better deal, cost less and get much better discount.
The very small feature differences are absolutely nothing to fret about.
And according to my sources, they use the exact same parts from the same provenance, for what it's worth.
The Integras are sold only through bricks & mortars stores from authorized dealers only with a premium price for longer warranty, but that's it, the clock stops here.
Integra DTR-7.9 is exactly the same as Onkyo TX-SR806.
DTR-8.9 = TX-SR876.
DTR-9.9 = TX-NR906.
DTR-6.9 = TX-SR706.
DTR-5.9 = TX-SR606.
DTR-4.9 = TX-SR506.
The Onkyo 805 vs the 875 difference is mainly the HQV Reon video processor in the 875.
The 805 is the same as the Integra DTR-7.8.
And the 875 does not have an equivalent Integra model.
The next Integra, the DTR-8.8 is the equivalent of the Onkyo TX-NR905.
If you want to know about the small differences between the Onkyo and Integra models, just download their manuals.
If you want to see the difference in feature/spec between the Onkyo TX-NR906, TX-SR876 and TX-SR806, just click here -->
http://www.faqware.com/Receivers/Onkyo_receiver_comparison_2008.html
LOTR