I have stayed at both these hotels many times and overall I prefer The Peninsula at suite level. The suites at The Oriental are all individually designed, so you can find yourself in a good suite one time and a really dowdy one next. I dislike all the suites in the Author's Wing - they are dark, dismal and poorly furnished and the bathroom plumbing is appalling. The suites in the River Wing tend to be better as they have river views, balconies and are much lighter. You do, however, have to find something that appeals to you decoratively as all the top suites are themed.
Although the suites at The Peninsula are nothing special in decorative terms, they are comfortable, although I don't like the little balconies they have, which are very badly designed and dated.
What I do like at The Pen are the restaurants, the pool and the spa. The only restaurant at The Oriental that really impresses me is The China House. Last time I stayed, even Lord Jim's was a little disappointing. It will be interesting to see if The Oriental improves or declines now that Kurt Wachtveitl has retired.
The Pen's spa is beautiful and much more up to date than The Oriental's, which was state-of-the-art when I first went there, 2 weeks after it opened, back in the day, but is now a little seedy and insensitive. But although The Pen's spa is spectacularly designed, the treatments are less so - mass-market Espa.
The Pen's pool is designed like a klong and has raised salas with integral fans. The Oriental copied this when they redesigned their second pool and although it is nice, it is overlooked by diners at the Verandah, so is not as private as The Pen.
If you like the historic look, then you will not go wrong with The Oriental. Both it and The Pen are very good urban resorts.