My boy just took your two critters and several others with a .284 Win and 140 gr Barnes Triple Shock bullets at just over 3000fps with no problems, all one shot kills but the kudu needed a finisher for a high shoulder shot. You mag will add a couple hundred fps to that so of course its plenty of power with a good bullet.
Take the gun you already own, save the money you would have spent and shoot one or two extra animals while you are there!!!
I used a 7mm Rem mag with 140 gr Ballistic tip handloads on my first South African hunt. My Kudu and Blue wildebeest were both one shot kills, and the wildebeest simply dropped in his tracks. On my second South African hunt, I again took a 7mm Rem mag, but with 160 gr Accubond bullets. I hunted several properties on that trip, and one PH, who also hunted with a 7mm Rem mag, commented several times on the large internal wound channels that the Accubond bullets made. Like Drivenhunter posted, "Bullet placement is the key to any hunting."