It is a good comp-and we kicked that one around WBW.
IMO Rice was a borderline guy too-and I was on the fence but eventually thought he should be in. And took him his entire time allowance (15 years) to get in. Rice beats Allen in most if not all counting stats, Allen has the edge in rate stats. I could be talked into Allen and to be fair, didn't see a lot of his NL career, but followed him through the sports pages, he was more hype than great hitter. Rice in 15 years got top-5 MVP votes 5 times, Allen twice.
I think relative to the time they played Rice was the better hitter and probably more deserving of HoF honors than Allen.