I own a lot of rifles. Included in my collection is .30-06, 6.8 spc, 6.5 grendel, .25-06, a couple .223's, .308's etc. There is one that I want to buy that I just can't seem to find around here. In my opinion it will do anything that I want it to do with very low recoil. That is the .260. I have taken elk with my 6.5 grendel and a 100 grain bullet. I would love to have a rifle that can throw a 140 grain bullet even faster. That will get you the range of the 7mm with a fraction of the recoil. White tail are extremely easy to kill and I think 7mm mag is way overkill on them. If you like getting smacked by your gun then the 7mm mag will do the trick just fine though.
The .260 is a little less common and it sounds to me like you aren't a reloader so depending on the stores you have available to you the 7mm mag could be more available in factory loadings.
Also, if you do reload, 7mm mag brass does not last more than 3-4 firings.