England or Ireland

They are both very different. there is an overwhelming variety of places to see in England. Ireland is more small villages, B&Bs and wilder countryside. Depends what you want to see.

I notice that you left out anything related to attractions in the cities. If you want diversity of sights, you'll have better options in the UK for a busy 9 day trip. I started to suggest an itinerary for you but you would probably be better off going to the Great Britain Heritage Pass site and seeing what is covered by their card. It has many of the estates, manors and castles included. It doesn't have many types of gardens from what I've heard but they have some. Big name castles are Edinburgh, Bamburgh, Conwy, Caernarfon, Warwick, Windsor, Dover.... The list is endless. Blenheim is the quintessential manor but they are everywhere. Countryside options are everywhere. The Cotswolds win most points for looking like what Americans think England should look like. On nine days you will have to be very busy.

Nine days isn't much for either Ireland or England. Three weeks will just about do it for the RoI, but you won't realize how repititious it was until you've done it. It doesn't have much in the way of castles. Everything you've read about is scattered all over the place. I don't know what to say about England. I've been chipping away at it for a long time (well over a year, cumulatively, in a couple or three dozen trips ) and still have to keep going back for stuff I've missed. Everything that you're interested in is scattered there, as well (Ken's post lists a couple of spots close to London, a couple in Wales, one in Scotland, and one way to heck and gone in the north of England). To me, what you're asking about screams Wales. The border's a couple of hours from the London airports. Three hours of road time allows you to stop at Stonehenge, Avebury, or whatever suits you fancy along the way and still have not so long a first day. If you make your first castle stop at little Chepstow, you can figure out how a real castle is supposed to work. Working around roughly the coast clockwise, gets you Caerphilly, Kidwelly, Pembroke, Harlech, Caernarfon, Beaumaris, and Conway. These are my idea of the best, but there's at least a hundred others. Wales is compact, the whole castle loop is only a bit over three hundred miles - - you could do it in four days. Make it five and you can do some detours along the actual coast (which beats Ireland for ruggedness; e.g., the Pembrokeshire coast) and spend some time in the Porthmadogs, Pwilhelis, and Betws-y-coeds.

From Conwy back to London is a hard four hours, maybe five. I'd take two days and go south through Snowdonia and the drover trails in the center of Wales for some really great scenery. If you pick and choose a bit (skip Pembroke and Beaumaris, don't be tempted by the Cardiff castle, don't miss Harlech) you could even worm in a couple of days in London - - or stop in the darn Costswolds or Bath or something.

Although I LOVE Ireland, from what you say you want to see, castles and manors, I think what Ed said is right on, go to England. You will have a choice of so many more castles, manor houses, etc than in Ireland.