I actually just went through a similar search-- I tested the Away Bigger Carry-On, the Travelpro Platinum Elite 21" Spinner, and the B&R Baseline Spinner.

TL;DR: it's hard to beat the Travelpro Platinum Spinner. It has the best wheels and handle of the three, besting the Briggs in my opinion!

My thoughts on each:

- Travelpro: this was the first bag I tested, over a 4-day domestic trip. If it had come after the Away bag, I would have not looked any further. The build quality feels excellent! The handle is the firmest (the grip is chunky, but if you have smaller hands you may not be into it?), and it rolled well even on the extra-thicc carpeting of the hotel. I can't decide if the magnetic feature that locks the wheels in one direction is a gimmick or not. I honestly think the bag rolls and tracks more straight than even the Briggs, but since I did not test them side-by-side, I can't really be sure.
Where quality falls short is on the zipper of the included removable suiter. It can get stuck and feels just average. However, the zippers on the bag itself feel as good as the Briggs. This is also the only bag with three solid and easy-to-reach handles (top, side, AND bottom-- super handy when lifting the bag up to the overhead storage).
Style is subjective but I really liked the gray with brown leather accents as well. The warranty of the new Platinum Elite bags is equivalent (at least on paper) to B&R's lifetime warranty and includes airline damage!

- Away: I tested this second, on a shorter 2-day trip.
I really REALLY wanted to like this bag. I love the look of it, and how well it pairs with their other accessory bags (backpack, daypack, and everywhere bag). In fact, I purchased the leather everywhere bag with it and they looked awesome together. Unfortunately nothing about it *feels* as good as the bag looks. The zippers are supposed to be YKK, but the pulls are small and feel far less solid (on par with a Samsonite/Tourister/everything else that costs around $100). The zippers on the inside (on the left-hand compartment liner) is way crappier. This one got stuck anytime I used it. The lining itself is thin and doesn't look like it'll hold up. The handle was even more underwhelming. You should have seen this mentioned in other reviews. It's flimsy and has way too much side-to-side play. The wheels are fine but let down by the handle. When walking through the airport I had to actively "steer" to keep it in line-- something I did not ever think about with the Travelpro. As with most hardsides, the bag doesnt have a bottom handle for ease of lifting or lowering it from the overhead storage. As luck would have it, the bag was gate-checked on the return flight and it was enough to scuff it on two corners. Some people say they like this- akin to aged/worn leather goods, but I disagree. To me, the bag loses it's good looks with scuffs and scratches.

What made this all worse was the quality of the $325 leather everywhere bag. The zippers were awful and stuck, but the biggest issue was how easily I accidentally ripped the stitching on the lining of the front pocket.

With all of that said, I do think the Customer Service from Away is great. I bought (and returned) the bags at the Chicago location, and they were a pleasure to work with. They acted surprised that I did not like the zippers ("since they are YKK") and completely shocked at how the lining of the leather bag had ripped. I also witnessed folks coming in to drop off/pick up luggage repairs and they seem to really take good care of everyone. I liked that.

- Briggs & Riley Baseline: this is the bag I'm using now, for the first time on a 3-day trip. I was familiar with it from having borrowed a friend's once and knew they're great quality. The handle feels good (great, compared to the Away's), the wheels and walking with it is great, and the overall quality feels solid and substantial. I also like the built-in suiter better than the removable suiter of the Travelpro, but this is not needed by everyone. The bag has these sleek fabric handles on the side and on the bottom. They are functional and feel super solid, but they're hard to find if you're not used to the bag. The Travelpro has normal handles on the side and bottom and it was just more intuitive.
Considering the going sale price for the Baseline and the Travelpro, the Travelpro is easily the one to have. I happened to score the Briggs for $300 off (it was a return!) and in perfect condition with all tags still on. Probably the biggest advantage this bag has over the Travelpro is the compression system. It may seem gimmicky, but it works super well! If you are not a good and careful packer, this feature may make this a better fit for you.

I also played with Tumi's Alpha 2 (Continental and International) spinners in stores. The handles and wheels were no better than Away's, but the zippers and lining felt decent. I honestly wanted to like them more as I like the look. However, I could not convince myself to pay more than B&R money for a bag that was only better than the Away in feel and quality (but cost 2-3x more).

Let me know if there is anything I can clarify or expand on. Good luck with your search!