I know everyone's tastes vary, so take that into consideration when I offer our opinion. We've eaten at both several times within the past couple of years. When Raglan Road was brand new it was was wonderful! Meals, desserts, service...the whole bit. In the past year, we've tried it twice and have now vowed never to return. Service sucked, appetizers and entrees changed and not for the better and, again our opinion, the condition of the restaurant was not at all clean. We'll go back for desserts...but not in the near future.
Rose & Crown we loved, menu changed, we hated, now is pretty good again the last two times...meaning food, service and just general cleanliness. We plan on trying it again. I think you'll be glad to be celebrating a special occasion here.
But I'm not really answering your question. Are they similar? Not really. The pub is more "pubbish" meaning good, but loud entertainment and lots of people participating in liquid libation at RR while RC is more "Disneyish" meaning a quieter meal. We love talking to the servers at RC as most of them are visiting from the UK. Expect tons of kids at both. They seemed less well behaved at RR for some reason.
Hope this was of some help.
