[Note: this information is current as of the time I am posting it. If you're reading this after the release of Endwalker, it may no longer be accurate depending on what changes SE implements.]
Right now, the general consensus in the player base is that leveling DoH via the Firmament is the best way to go. Here are some reasons why it's not.
Recipe difficulty is substantially higher than other recipes of the same level without similar increase to XP earned. Let's look at level 60 recipes as an example.
Firmament recipe - 956 Progress, 15702 Quality, 60 Durability.
Min XP reward is 1.28 million for 300- 849 rating. Mid tier XP is 1.42 million for 850-1319 rating. Max tier XP is 1.77 million for 1320+ rating.
House of Splendors recipe - 956 Progress, 7851 Quality, 70 Durability.
Min XP reward is 1.27 million for 400-549 rating. Mid tier XP is 1.4 million for 550-709 rating. Max tier XP is 1.53 million for 710+ rating (note this max rating is lower than what's required for Firmament's mid tier ).
Typical recipe for leve - 1116 Progress, 8377 Quality, 80 Durability.
XP rewards will vary by leve but average would be around 1.3 million for NQ, with XP doubled if you turn in an HQ item. You're free to only repeat the leve that rewards the greatest amount of XP for that level if you want.
The increased Durability and lower max Quality on the Splendors and leve items makes it easier to craft those items to what's needed for their max rewards than it is to craft the Firmament items to the mid tier rating (which will reward less XP than max on the others). Fewer steps is more items turned in faster, and so more XP earned faster.
Firmament offers no way to get DoH gear upgrades that you will need to keep up with increasing recipe difficulty as you level higher.
House of Splendors will reward Yellow Crafter's Scrip in addition to the XP that can be used to buy gear for levels 58, 60, 65, and 70.
Leves will reward gil in addition to the XP (and shards/crystal/crafting materials) that can be used to buy gear from the MB or NPC vendors
Class quests will usually provide either primary or secondary tool appropriate to the quest level plus a second piece of gear in addition to XP.
Crafting your own gear is an option if you have the right classes leveled high enough but it can be difficult to keep everything about the same level while leveling. Usually you'll be forced to rely on the MB or a vendor to get most of your gear.
Firmament offers no way to obtain Master Recipe books.
One of the big draws to crafting is the ability to make your own gear and housing items, many recipes only being learned through the Master Recipe books. The level 60 and 70 books can only be purchased with Yellow Crafter's Scrip (level 50 books are obtained in Mor Dhona by crafting specific starred recipes as HQ items). The Master 3 books also contain the recipes for the items needed for most of the level 60 and a few of the level 58 class quests (though you can always buy the items off the MB at massively inflated prices as other players take advantage of those who can't buy the books).
There isn't really a good way to earn gil by leveling DoH in the Firmament.
How are you going to pay for the materials needed to level if you haven't already leveled up your gathering classes?
The items you make for Firmament can't be sold to other players. You can buy vanity items with the Skybuilders scrip you earn to sell on the MB but most players who are leveling would prefer to buy those items for their own use. The amount of Skybuilders scrip earned from the leveling recipes is fairly small compared to item cost. It's going to take quite a while to get enough scrip to buy that mount you want.
Items crafted from normal recipes may reward less XP but you get the additional benefit of being able to sell to other players to earn gil to use as you want, including buying gear upgrades or materials as you level.
Overall, you're getting less out of leveling via the Firmament than you would be getting by combining the other ways of earning XP.
A lot of players leveling via Firmament ignore the class quests until after they reach level cap, which is crazy. Class quests are worth almost the same XP needed to level up at the quest's level in addition to rewarding gear and shards/crystals.
As an example, it takes 9,593,000 XP to level from 68-69. Doing the level 68 class quest rewards 9,578,250 XP, a choice of Grade 5 materia, 250 crystals (type depends on what the class uses) and a secondary tool. You're also going to get additional XP crafting the items needed for the class quests. There's 18 class quests that reward significant amounts of XP. That's 18 levels you had to work harder than you need to because you skipped doing them.
If you hold off on doing them until you reach max level, all that XP goes to waste not to mention you've delayed access to Manipulation (level 65 quest reward), which makes a big difference on higher level recipes.
Grand Company Supply missions are worth 1-3 levels each up until about level 65 when XP earned starts to drop compared to XP needed to for next level. That's a nice once a day boost for crafting a single item if you take advantage of it
Leve XP tends to be much better per item turned in than the Firmament Collectables (CUL and to a lesser degree ALC can be exceptions. You are limited by the number of allowances you've accumulated so use them sparingly until you reach level 71 when you will no longer have regular class quests for XP and the supply mission rewards are a smaller percentage of XP needed to level.
House of Splendors XP is on par with or slightly better than what you can realistically expect to get from Firmament not to mention you'll be earning yellow scrip to buy leveling gear and other items used in crafting. You will need to pick up a one time quest in Ishgard once you reach 50 on any DoH class to unlock House of Splendors in Mor Dhona and the ARR city states (does not need to be repeated for every class), then do brief quests to unlock each Splendors location and its related categories (won't have access to the level 70 options at the Limsa Scrip Exchange unless you've unlocked the Rhalgr's Reach Splendors as an example).
The Crystalline Mean quests are available once you reach level 70. The drawback is that they are one time and shared between 2-3 DoH classes but it's still very good XP and rewards a nice amount of yellow scrip for the relatively small effort each quest requires. Again, easy XP that you shouldn't let go to waste while leveling.
The crafting beast tribe quests offer good XP (will scale to your class level up to the level cap for the expansion where they were introduced so you'll usually get a half a level per set of dailies) and supply the materials you need so they can also be worth doing. Their big drawback is they require a fair number of zone side quests to be completed on a DoW/DoM job before they can be unlocked and they're only viable for leveling during the levels introduced in their expansion. Unless you want their rewards (like class quests, why let that XP go to waste?), I wouldn't go out of the way to use them for leveling.
Could The Firmament still be the best way for someone to level DoH?
Depending on their personal situation, yes. The Firmament isn't a bad way to level, it's just not the best overall.
If someone isn't interested in moving into mainstream crafting and just wants to obtain the Skybuilders Scrip items, then leveling in the Firmament makes sense since they will earn scrip as they go.
If you really hate moving around to different locations to turn items in, Firmament may be better because you'll only have to travel between it and a marketboard to get more materials when you run out (though the same can be said of House of Splendors once you have it unlocked at 50).
The Firmament is also good for players that find themselves constantly struggling with inventory space since there is a very small number of different materials to have on hand compared to normal crafting.
I would recommend that everyone leveling DoH use level 40 Firmament recipes for levels 50-52 even if I don't recommend it at other levels. Recipe difficulty takes a bizarre jump as you move from ARR into HW content. DoH gear from the original level 50 end game is not cheap to buy or easy to make, and the level 51 crafting gear doesn't quite compensate adequately for the increased recipe difficulty leading to frustration. The level 53 gear in line with what it needs to be for crafting at that level so that's a good time to switch back to other methods.
Please feel free to share your own leveling experiences and recommendations for others to who are looking to level crafting and gathering before Endwalker's release.
This is also a bit of an eyesore because of the length. Suggestions of ways to improve formatting are welcome.