You will find advocates for both breeds. In many instances personalty and egglaying varies as much within a breed as it does between breeds. It all depends upon the source and genetic background of the birds that you select.
Are we talking hatchery stock or breeder quality stock? Hatchery stock varies wildly. You can have bad and good in both breeds, of course.
This has been my personal experience with both breeds:
I've had both RIRs and BRs, in hatchery stock, as well as show quality stock. The BRs lay every bit as well as the RIRs in both types. I have 5 year old BR hens, progeny of hatchery hens, laying regularly about half of the year, and I mean 4 egg per week each.
My show type RIRs were much larger, but much more docile "mind your own business" types, than my hatchery RIR hens, though both were excellent layers.
My BRs of both types were friendly birds. Barred Rocks are my all-time favorites. I no longer have RIRs--the hatchery hens died from internal laying and ovarian cancer and I sold my breeder quality hens in a downsize. I'll always have BRs.
Can't say that I've ever noticed a terrible lot of difference between the two in terms of their production, egg size, or shell color.
I'd have both myself, but if I had to be limited to just one breed I'd go with Barred Rocks, but that's because I think they are prettier.
Amongst the major historical dual-purpose breeds that once had a major role to play in American agriculture - Rhode Island Reds, White and Barred Rocks, New Hampshires, and Delawares - I cannot say I find much difference in egg production, size, or quality from any of the sources I've had them from. None are really selected for any longer for the qualities that made them famous to begin with. So go with whatever you like the looks of most.