I own neither a .243 Winchester nor a .270 Winchester, but I like these calibers.
In my country, the .243 Winchester is quite popular among roe deer and fox hunters during summertime. A buddy who guides several hunters every year for roe deers told me he saw many Blaser K95 in .243 Winchester in hands of roe buck addicts. He also loans a Winchester XPR in this caliber for people who don't have their own gun.
The .270 Winchester is a bit less popular, but not rare. Many mountains hunters still use it in rifles like Tikka, Blaser (R93, R8 & K95) and others. I also saw some Browning Bar's in this caliber for driben hunts, but far less than the .300 Winchester magnum.
In UK, the .243 Winchester is also very popular for deer hunting. I hunted muntjacs, chinese water deers and fallow deers with it with several rifles chambered in this caliber.
In Namibia, the .243 Winchester is very popular in the southern part for springboks, bul also gemsboks, even if most of farmers shoot them in the head.
I had the opportunity to use it during a springbok culling. The farmer gave me his rifle that was a Brno ZKK 601 rebarreled with a heavy stainless barrel in .243 Winchester. Ammunitions were loaded mainly with Nosler BT 80 gr and it was incredible how effective was this combo, even above 300 meters.
The .270 Winchester is also appreciated in the southern part of this country. I bought a Tikka in this caliber to a Namibian girl ans she has hunted many animals with it.
I saw another girl hunting many animals up to a big waterbuck bull with her Tikka and Hornady CX 130 gr. She had a full success and I also had the opportunity to use this rifle on a young blue wildebeest cow shot at around 200 meters. Dropped on the spot. It won't be my fist choice for a big eland bull, but with a good quality bullet, I won't hesitate to use it again on all plains game.