Huh? John Jay and Adam Eaton aren't even comparable. Eaton is a 6 WAR outfielder with pop, and a mighty consistent 115 wRC+ hitter and plus defender at 27. Jon Jay is 31, had a 57 wRC+ in 2015 and had a whopping .371 BABIP last season. He's clearly going to regress back to replacement level. He's not even as valuable as Zeke Carrera for goodness sake
This isn't JON Jay vs Adam Eaton. Jay is a buy low free agent that can be signed short term to give the youngsters a little more seasoning in AA/AAA. Eaton is a sell high candidate who will likely cost more top young assets than he's worth moving forward.
If Adam Eaton is a 6 WAR player I guess that means Kevin Pillar is considered a 5 WAR player??. He's a good little player but very few players can be 6 WAR on a yearly basis and I don't think you can reasonably expect Eaton to maintain that level of production over the rest of his career. How many Outfielders have put up back to back 6 WAR seasons? Only the elite of the elite can be good for 6+ WAR every year (aka Mike Trout). If you look at the OF who have had a 6 WAR season they usually see a significant regression the following season/and or seasons. Eaton had a career season but history isn't kind to players like Eaton.
Let's look at the OF who put up 6 (or close to 6 War) in 2014 and what has happened since. I'll leave out Bautista since he's much older.
Brantley went from 6.0 to 3.7 to the DL
McCutchen went from 6.8 to 5.8 to 0.7
Gordon went from 6.4 to 2.7 to 1.2
Stanton went from 6.3 to 3.9 to 1.7
Gomez went from 5.7 to 2.7 to 0.9
Jones went from 5.5 to 3.6 to 1.4
Puig went from 5.4 to 1.5 to 1.0
This is just one example but i went through all the other years and the drop offs after 6 WAR seasons were similar. All the data points to Adam Eaton being a 3-4 War next season. That's still a very solid player but I'm not paying a kings ransom for a 3-4 WAR corner OF who is likely to regress even more in future years.