I would say no. While many respected paleoers on here do insist on grassfed, I've never knowingly eaten a grassfed animal (notwithstanding the fact that even conventional beef in the UK is fed grass an awful lot of the year) and feel completely comfortable with the 2g of omega 6 I get from my 500g of relatively fatty beef most days. One point of contention is that NutritionData (and the charts you link to look identical) suggest that grassfed meat is substantially less balanced than typically suggested. Indeed there's virtually no difference between the meats according to those measures. This has been dismissed as "frankly impossible" here with this source (from a purveyor of grassfed meat) suggesting that grassfed contains even more omega-3 than omega-6. In any case, if omega-6 is all you're concerned about, then conventional beef is still far better than the finest pork, chicken or turkey. Any nut or seed apart from macadamia nuts will be worse than these.
Of course, eating non-grassfed means that I don't get hardly any omega 3 from it, so I eat wild tinned salmon for the rest of my protein and/or take fish oil. Most of my omega 6 comes from the butter (2.7/100g)that makes up most of my calories, in fact. Because of the butter I don't feel I'm missing out on CLA, vitamin K2 etc either. Similarly, it would make no sense to choose grassfed on the basis of getting less SFA, while I'm getting most of my calories from butter, which contains substantially more SFA relative to both MUFA and PUFA than meat. Grassfed, being leaner and higher in PUFA might be better for Cordain type paleos therefore, but for high SFA paleos, very much less so.
One thing that might be a factor that would recommend 'quality' meat would be the avoidance of assorted other chemicals being pumped into the animal, but this would be a reason to go organic, not grassfed per se; notably I've not seen any definitive evidence or argument either way, for there being a major health issue here.