Empyreans Ease and Popularity

The 10th Vana'diel Census confirmed what we all already knew, that Empyrean weapons are far more numerous than Relic weapons and of course the disproportionately difficult Mythic weapons (I hate it when people call them Mystics...). They take so much less time to bring to a usable level than relics and mythics that it's hardly a surprise.

Time
On top of the overall faster acquisition is the fact that Abyssea time was not and certainly is not a limiting factor anymore. That means that you're almost always able to work on your Empyrean for as long as and as frequently as you're able to play FFXI. Technically if you consider farming gil to buy currency equal to working on your relic/mythic then the same could be said for those types. However, one of the most efficient ways of obtaining gil IS farming currency, so it's not exactly in the same league.

Difficulty
The seperate paths of Empyreans have notably differing levels of difficulty. For the weapons the trophy stages are:
Glavoid - Itzpapalotl - Orthrus (Dagger, Great Axe)
Chloris - Ulhuadshi - Dragua (H2H, Polearm, Scythe)
Briareus - Sobek - Apademak (Sword, Katana)
Fistule - Bukhis - Alfard (Axe, Bow, Club)
Carabosse - Cirein Croin - Isgebind (Great Katana, Gun, Great Sword)
Kukulkan - Sedna - Azdaja (Staff)

Since the instrument and shield don't have NM and VNM stages their difficulty is different, but for those:

Iron Plates - Colorless Souls - Azdaja/Apademak (Shield/Harp)

For weapons the La Theine path is generally considered the easiest overall path and Tahrongi the hardest. I agree with that consensus and would add that both Carabosse and Cirein require few people to kill and can both be solo'd. Carabosse would take a long time, but it can be done. For shield/harp I'd consider them overall to be harder despite having fewer trials, because of the VNM system which artificially creates more competition and forces a longer time to completion unless you get a lot of help/extra T3 pops.

Soloing
Yes, you could buy trophies from groups that don't need them, but with the exception of Fistule, Cirein and Briareus there are no easy ways to get Empyreans solo (if that even counts as solo) unless you brew everything. If you have trouble getting help then your best bet is farming the popset yourself and trying to trade upgrade items for help. I don't know if the "[NM] farm. Trophy: X. 1/?" shouts really work. I imagine you'll have a hard time getting competent helpers since most dedicated players will have the majority of their AF3 upgraded.

As for brewing. Cruor farming is pretty fast with 2 or 3 people. Enough that you could get 100k+ in a short evening of play. Some NM's are easier to brew than others, but if you really had to you could manage doing it all completely solo. It'd take you a long time of hardcore cruor and popset farming, but the fact that the Abyssea system makes it possible to be 100% independent if you had to, makes a big difference.