I am a long time LR user, but started shooting with a P45+ recently. I certainly have a bias tpwards LR, as it is a program that perfectly fits my needs, want and aspirations.
What I would suggest that LR works perfectly well with the P45+. Default rendition maybe better on Capture One, but both programs can be tweaked a lot, so it is hard to say which one is better.
I made a few long exposures recently, and what I see confirms my views. Not a lot of difference, C1 does more aggressive noice reduction.
C1 also gives a different standard tone curve, especially with 'film curve', but once you balance out the subject I would say that it is not a lot between he two products.
You can open and work Phase One files in 4.x of LR or CS6 ACR if you are not shooting a IQ2. If you are working with a DF or DF+ and are not going to shoot a LCC then you should have no problem. If you are working tethered to one of these cameras, then as mentioned Capture One will be necessary. To process raw files from any Phase One, you can use LR, 4.x or higher (3.x on older backs like P45+) or ACR.
Note if you are renting a P45+ and wanting long exposures, I would stay with Capture One as I believe it has the best noise to detail algorithms for processing out a long exposure from a P45+.
Most times I start in Capture One as with vr 7 the Phase files seem to just have a much better look than output from LR.
You did not mention the back being rented. If you are renting an IQ2, i.e. 260, 280, then so far I have not been able to open the 260 files in LR 4, and I have not upgraded to LR5 yet so I don't know if they work there. However all older backs will work in 4.x Just checked, it takes LR 5.2 to work with 260 files, there is no mention in the RC notes about 280 files.