Fabricate Claims using spies is the far more efficient way of doing it, at least when you're playing to creat as many PUs as possible (I have 27 atm in my current game, had 30 odd earlier, & have inherited about a third of Europe so far).
I only Claim Thrones at game start, before spies become easier to gain, & before I have a lot of PUs on the go.
The big problem with Claiming the Throne using a Royal Marriage is it costs you minus 100 to relations with all other PU allies. That is a very very bad thing because if your ruler dies the PUs end if you have negative relations with the PU junior. Also, your chance of actually inheriting is better the higher relations are.
So, imagine if I were to Claim a Throne with 27 PUs ... I'd then have to spam diplomats to 27 nations to get relations back up. Claim Throne twice & most of those are in negative relations, meaning all the PUs mght end if my ruler were to die. (Though frankly I'd restart).
Fabricating Claims causes no real loss to relations with other PU allies (well, maybe -5 for declaring war). There's also no legitimacy loss (though that's a minor issue later in the game). In my WC attempt game, I avoid having RMs with anyone, to allow me to declare war more freely, & fab claims on anyone I can. I'm even releasing monarchy vassals so as to open them to fab claims.