The 1D line was Canon's flagship line on DSLR. They only very recently (within the last few months) came out with their first mirrorless flagship, the R1.
The R1 is in some ways only an incremental upgrade to the R3, and many people wondered when the R3 came out why Canon didn't call that their flagship. Probably because it didn't hit all the marks for Canon.
As for your question, the R3 has probably dropped in price now that the R1 is out. And yes, the R3 is better than the 1DX III (with some notes) and worth getting. The R3 even has 1 stop better dynamic range at ISO 100 than the R1.
The R3 is best at full electronic shutter, where it can do 30fps which is much higher than the 1DX III. The 1DX being a DSLR obviously has an optical viewfinder and the R3 has an electronic one. The viewfinder on the R3 is very decent and has eye controlled AF selection as an option for who like that (doesn't work perfectly for everyone, but for some it does). Battery life is less than the DSLR because of the electronic viewfinder, but the batteries are big and last very long. Autofocus is great in the R3.
The main things the R1 has over the R3 is a bigger viewfinder, pre-continuous shooting (saving images from before you full press the shutter), and an even faster, better focusing sensor (at the cost of 1 stop of dynamic range at low ISO). In all other respects, the R3 is essentially a flagship camera way beyond the capabilities of the 1DX III. It's also much lighter as a gripped body than the DSLRs, surprisingly light.
