I've shot blue and black wildebeest, red hartebeest, kudu, Hartmann's mountain zebra and waterbuck (to name just the larger critters) with the 6,5x55 with good 140-grain bullets with no problems whatsoever. I've shot a bunch of critters with the 7x57 as well, up to kudu and wildebeest.
Eland is probably too much of a step up, but many of them have been shot over the years with the 7x57. Good bullets and good shot placement are essential here, just as they always are.
The 6,5 Swede worked well, and the 7x57 should be at least as well, if not better. I would stick to 160-175 grain quality bullets.