I consider these to be the best two places in town. Here's a brief comparison, based on two very recent visits.
BP has a 5 course prix fixe menu for $89, (they now do a $59 3 course for early sittings), you choose app, entree and dessert, soup and salad are same for everyone. They also do wine pairing for each course (3 levels at $39, 55 or 89), or order your choice of wine.
RO: apps, entree and dessert all at individual prices on menu, and choose wines yourself.
Food: Overall, both are very good to great.
Most recent visit to RO, I started with a cajun-inspired prawn appetizer, duck entree and bread pudding. Prawns were great, but the accompanying dumpling/samosa-like item could have been a bit crisper. Duck breast was perfectly seared to medium rare, and nicely spiced. Came with a squash hash that was good, some veggies, and a fried risotto cake that was kind of mushy. I don't know if a fried risotto cake can be done well, so this is probably as good as it gets. The bread pudding- one of the great desserts anywhere.
BP, my app was a "soft shell taco" - a flat tortilla with a too-big pile of bean, a chunk of lobster, avocado, a nice spicy sauce...quite good. Soup and salad you was a spicy squash soup with pumpkin seeds, apple jelly, some kind of oil. Extremely good! Salad was mixed greens with beets 3 ways - one chunk of roasted beets, some fried beet shavings, and beet powder on a champagne mousse cube. Interesting, innovative, and good. My entree was duck breast on soba noodles, miso broth and shitake mushrooms, with enoki tempura on top. Tempura wasn't totally successful, as it was a clump of enoki (much easier than a bunch of incividual mushrooms). Duck was great, noodles and miso could have been a bit more flavourful. Dessert: shaved frozen blue cheese, port ice cream sandwich and a blue pear (small pear in a blue curacao gel). Odd, good, odd...not sure how to describe it. Wine pairings for the meal (did the mid-level one) worked well.
Both nights, everyone I was with was happy with all their food - so I would say my opinion here covers that of my wife too (others people not same at each place, so can't compare).
It would be really hard to say which was better. RO is more simple, great food. Less innovative, and less expensive. I don't think their wine list is spectacular, and given that they have a pretty consistent menu and small by-the-glass selection, I find it odd that they don't always mesh well. For example, it has now been rectified, but for a while they didn't have anything that worked well with their duck...they've now added pinot noir to the by-the-glass list, but previously the reds were more for the beef/lamb dishes.
BP, I like the 5 course concept, and I like the wine pairings. I also like the fact that they change their menu monthly. The food is more innovative, and I like that the chef tries a lot of new ideas with flavours, textures, etc. But sometimes everything doesn't work...sometimes a simpler idea might have been better. So, while the food may be (only slightly) better at RO, I think they are pretty evenly matched.
Atmosphere: I prefer the RO, for its semi-rustic diner feel. More relaxing. BP is too stark, cold and bare. But they are working on that, with some re-designing going on.
Service: great at both. RO a bit more casual, the odd glitch (plates to wrong people, forgot coffee...). BP - more staid, but still fun and friendly, no mistakes at all.
Price: BP is more expensive by far: $89/head. The new 3 course meal gets you soup or salad, entree and dessert for $59, but as the menu is really designed for 5 courses, that would be a small meal. Most recent visit, 3 people, 5 courses and mid-range wine pairing was about $460 before tip.
RO an average 3 course meal would be in the $50 - 65 range, but it would be substantially more food than the 3-course at BP. Last visit was 4 people, all but one had dessert, 3 or 4 beers and 2 bottles of wine (about $60/bottle) for well under $400 before tip (360 or 370 I think). For that much food and booze, you can spend close to that much in a lot of places in town and get far worse food, wine and service than you experience at RO, whereas BP is sort of in its own price category for Edmonton.
Hard to make a choice on which I prefer. RO might win on just food, but BP gets it for wine, willingness to take chances (even if not 100% successful) and overall experience. Really, I'm just glad they are both here and I have to make an effort to go to both more often.