I haven't used the Yamaha or heard much about it, but I will toss out a few thoughts:
1. Both players offer similar media support (BD, DVD, SACD, DVD-Audio, CD, USB, Netflix, DLNA) and multichannel analog outputs. The BDP-93's analog section is unusually good for the price range, even moreso than the BDP-83's was. I don't know how the Yamaha sounds, but matching the OPPO in this price range would be impressive. If you are really serious about your analog performance, the BDP-95 should be out next month and will offer a 7.1 analog output using a very high-end ESS Sabre32 DAC, but it will set you back almost $1,000. For $500, the BDP-93 has a
very good analog section. It also allows some internal bass management controls (user adjustable global crossover), which the A1000 does not.
2. The BDP-93 offers a few extra features that may or may not matter to you. One is wireless networking. Others are dual HDMI outputs and an eSATA port. Assuming you are going to pair this player with your AVM20, the second HDMI port is not likely to matter to you, but if you moved to an AVM50 or other HDMI-equipped Anthem and wanted to use this player with a 3D display it would become invaluable. Connectivity is otherwise the same (IR input, RS232, optical, coaxial, component and composite video), with the A1000 offering a dedicated stereo analog audio output.
3. The A1000 is listed as "3D Ready" (via firmware update), although it looks like the 3D support was added in a December firmware update. BDP-93 supports 3D right out of the box.
4. Yamaha doesn't say what video processor is being used, which suggests that the player's main chip is likely doing it. The BDP-93 is using a Marvell QDEO chip for video processing. This will give the BDP-93 an advantage with DVD and streaming video performance, although the impact for Blu-ray will be less significant. From looking at the manual, I would not be surprised to find that Yamaha was using a version of Mediatek chip as the "System on Chip" (SoC) processor for the A1000. There are some menu item labels that are very reminiscent of the Mediatek platform. OPPO uses Mediatek chips as well, although the BDP-93 is using a customized version of the latest chip and has implemented some things in firmware that Yamaha has not (such as the previously-mentioned bass management control).
5. At list prices, the BDP-93 is $200 cheaper. The Yamaha looks to be available from a lot of places for about $100 less than retail, though, which still gives the BDP-93 that $100 advantage you mentioned.
6. It's been years since I bought a Yamaha disc player. My last Yamaha (DVD-S1500) was burdened with one of the worst user interfaces I've ever seen on a disc player, something that slowly drove me nuts. I suspect the A1000 is better than the S1500 was in this regard, but the remote looks pretty cheesy (flimsy and cryptically-labeled). From looking at the manual, the A1000's menu
is somewhat better than the S1500's, but it isn't as straightforward a layout as the BDP-93. The manual is also much shorter and less informative than the BDP-93's manual. (General observation on user manuals: Outlaw has offered the BDP-83SE in bundles with some of their products in the past, but they did not choose to prepare an "Outlaws' Guide" to that player. In contrast, they have written such guides for Onkyo, Marantz, and Velodyne products they've sold over the years. The reason is simple. The OPPO manuals are at least as good as Outlaw's manuals, leaving no need for supplemental documentation. I couldn't make the same claim about the A1000's manual or the manuals for those Onkyo, Marantz, and Velodyne products.)
7. If you are going to give any consideration to customer support in the purchasing decision, the BDP-93 is almost certainly the better choice (unless you have a really excellent local Yamaha dealer that you trust to take care of you for years to come).
Folks around here will probably not be surprised by this, but I'd lean toward the BDP-93 over the A1000. Some of that is from my experience with the BDP-93 (as documented
here) and some of it is from experience with both companies and their hardware.