I have been on a few Eland hunts, surprising enough, the majority were taken with a 308 and 375 now that I think of it. In fact, I have shot an Eland with a 308 successfully, but I was also on an eland hunt with my Dad where he shot a perfect shoulder shot on a big bull with a 375H&H and the vitals were not hit ... As with everything, context is required.
In short, I shot an eland with 308 with premium mono bullet, it was in the Free State in SA, meaning open terrain (take note), it was shot for meat, it was not a big "blue" bull and I itched to use this specific 308 as it was new and wanted to test it.
The big bull my dad shot. Terrain was open mountainous area, again not bushveld, but terrain did not influence the chose of firearm in this instance. Most people probably would have chosen something like a 300H&H, but the 375 is more than capable. Why was the vitals not hit? Purely due to the bullet. Unfortunately due to this incident we lost faith in the specific bullet (SA brand, so USA readers need not worry) and have since heard similar stories of this specific bullet. Just for interest sake, we had a 243 with us for smaller antelope and my dad used it for a high neck shot with a 243...
So, would I use a 308 on a Eland again? Well a lot of circumstances need to be considered, but in 99% of the time no. If I went on a hunt and Eland was on my list (specifically in bushveld areas), then I would prefer something bigger than a 308. However, lot's of hunters here hunt with only a 308 and then they run into an Eland (not having placed Eland on their list) and still successfully hunt one, some also wound them.
With a premium bullet and correct placement it (308) would do the job. Then again, as with my Dads Eland, with a 375 H&H and non premium bullet, even a 375 would leave you short.