Yes there is a huge difference. While the R9 neck is not as fat as the R8, it's still a baseball bat compared to the 60s slim taper profile. Whether or not this will be an issue for you will depend on how the neck feels in your hands. Definitely play it before you commit to buying.
It depends which 60's neck you are comparing it to. If you compare an R9 to a 90's Les Paul Classic with the flat back shape and .790 to .890 taper, it's going to be quite a difference. If you compare that R9 to an R0, which usually have more shoulder on the back shape and a taper of around .815 to .915, it's not going to be as big of a difference.
I decided I 'needed' a lemon burst Les Paul about a year ago, and having very limited local access, I spent a BUNCH of time pondering whether I should go for an R9 or R0 for exactly the the reason you're asking. Part of the driver for the indecision was there's much more choice in R9s and R0s 'tend' to be pricier.
What seems to confuse things further is that (I'm told) the production 60s neck is thinner than the CS 60s neck (and there are different versions of the CS necks on top of it). I'm used to Jacksons and I went for an R0 and it's great for me: even then, it's still towards the thicker limit for my tastes, so an R9 would probably have been a mistake..
It depends which 60's neck you are comparing it to. If you compare an R9 to a 90's Les Paul Classic with the flat back shape and .790 to .890 taper, it's going to be quite a difference. If you compare that R9 to an R0, which usually have more shoulder on the back shape and a taper of around .815 to .915, it's not going to be as big of a difference.
Trying to nail down "Gibson neck profiles" without actually holding the guitar in yer hand is a crapshoot at best. There were even several variations of the ever-bespoke-and-uber-sought-after original 59 burst. Three variations in that one year alone if my [studious] memory serves me correct (whether that's just a rumour adding to its mystique who knows; but considering I collect RIs and a couple real-deal bonafide originals, I've done my homework. And one thing that is consistent throughout the 50s and 60s and 70s and 80s AND 90s lineage of Lesters is...)
I have played a truckload of Les Pauls 59 historic reissues, CC`s R8, true historics (3) but no R0. So i can`t comment on the 1960`s neck. I loved the neck of the CC`17. I have a 59 true historic- fantastic neck too. The 1958 models had mostly a little bit too fat necks for my taste. The 1959 necks on the other hand were without exception very comfortable to play with the CC`17 playing like butter.
HUGE difference. I had a G0 and an R9 at the same time. The G0 was slim and flatter while the R9 is fuller and more rounded. The G0 is gone and the R9 will go to the grave with me..