For me it comes down to feel and whether I need the strings to thump or to "sing". If I need thump, I use an old set of Sadowsky Black Label Flats. They are currently on a Jazz Bass, but sound great on a P. It's too bad they are no longer made. They sound like Labellas, but retain their clarity once broken in. The set I have are 045 - 105, but I wish they were the lite version. I've ordered a set of the Labella LTF's.... I'm hoping these don't disappoint. Labellas, for me, tend to lose some pitch definition once broken in... I'm told these don't do that.... We'll see!
I've used the same set of old version Sadowsky Blue Label Flats for coming up on 5 years..... They "sing". The 040 - 100's have a bit more tension than TIJF's, and since they are on a hex core, they are a bit stiffer. They have that same mid focus as TIJF's.... But they don't have that soft, woody attack. Instead, the transient is a bit more aggressive, while not going into thump territory. These have been the perfect Pbass string for me..... I patiently await Sadowsky to re-release them. Edit.... I use these on a CS'59 P with stock pup.... But I've also used them on a P loaded with the Fender OV'62 pup with similar /great results.
I have a set of TIJF's on another P. I love them, but have to really pay attention to my technique when playing them. I'm not an aggressive player, but I will dig in occasionally.... If I'm not careful, they will fret out. I've just recently replaced these.... The previous set were 11 years old, and had been taken on and off basses so many times, they were pretty much shot. Break in when new is somewhat painful..... Overly bright when new..... And just rolling down the tone knob makes them sound a bit hallow. The good news is that I've used them for the last couple of gigs, and they are rounding out nicely.