BESVISOR

I'm bias given I'm a Travel Advisor but a good advisor is way more valuable than FHR.

The upgrades with a good advisor with great relationships are likely much better (over a number of bookings).
Hyatt Prive is usually upgrade at time of booking anyway.
With great relationships across: Aman, Rosewood, Four Seasons, Virtuoso, Prive, etc. Often, upgrade is done at booking for my clients (assuming it's not nearing sold out or festive/holiday dates).

Just completed 3 Aman bookings over the past 2 weeks and all were upgraded at time of booking.
COMO Parrot Cay upgraded at booking from a Two Bedroom Family Beach House to Two Bedroom Beach House (updated with bigger pool and private beach).
Rosewood Hong Kong upgraded at time of booking always and transfers. In June, two clients were double upgraded at booking by my RW friends due to booking higher suites.
A client recently just finished a stay at a FS in EU and was upgraded at check in into a suite which was over $20,000 in value for his stay ($5k+/night upgrade for 4 nights). That's an extreme example and certainly doesn't happen all the time. The same client was then upgraded at 3 other FS properties on the same trip in July and 2 were single upgrade and 3rd was triple.
In the interest of being fair and transparent:
I had clients go to Blackberry Farm in June and it was completely sold out so no upgrades were extended.
Same happened at Montage P.B. as well. Fully sold out so no upgrades were extended.
Clients stayed at a particular Santa Barbara property. Upgraded them at the time of booking but there was an issue during their stay which annoyed my client and I was very upset by it as well so I've followed up with management.

And perhaps one of the biggest difference is that a good advisor travels and can advise you on properties. I don't think FHR agents really understands the differences between one "luxury" property from another. You can see on the Aman thread that I just came back from Amanera again (paid full price) to review the property and testing it out for my clients and assess its current quality for COVID travels. Then booked 3 clients once they got feedback from me. Most of my clients are more time sensitive than cost sensitive. Assisting in choosing the correct property is a tremendous intangible value.
Just returned from Hotel Esencia and Chable Maroma and plan to head to Cabo in a few weeks. To check out which properties are ideal for my clients.

As another interesting point, many of the top advisors have clients with Amex Centurion access, yet, they still book through an advisor.
But as with all things of this nature, you need to find a great advisor that fits your needs and build a long term relationship so you're always on the same page and it's like calling up a friend to chat about travels and he/she knows exactly where to point you to and get you the most value. If your advisor happens to share the same taste as you then that's a huge plus/advantage in my book (the guidance will be more accurate/relevant). There are a lot of advisors out there and certainly not all are equal (the spectrum can vary widely from what I hear). There are some great ones here on FT, but I'd think the top advisors aren't always willing to take on just any new client either (due to bandwidth), I can't speak for other advisors but I'm always looking for great long term fit and less of a random new booking.
Being human, each TA will have his/her individual strengths and weaknesses so you'll need to take that into consideration.

Again, I'm obviously bias given my profession and the amount of effort I pour into my passion/work but I hope you'll find a good TA and the value you're looking for!