For Chelsea getting into Champions League after bad season last year is huge success and big relief for their fans. This means they will have much more exciting and important time playing next year with other best English teams. Their better and more steady play at end of season clearly helped them when it mattered most.
On other side it mix of good and bad news for Nottingham Forest. It is tough to have been in top three for so long and then play worse at end. But getting into Europa League is still big deal especially since they started season so poorly. This shows they are very tough and got much better as season went on.
From any point of view, Chelsea deserve to be in the Champions League more than Nottingham there have been a lot of changes at Chelsea over the last few seasons and their games are more interesting, basically deserves to compete in the champions league. Next season EPL will be the luckiest league with the most representatives so it can increase chances of winning compared to other leagues, almost all the best clubs go to UCL except Manchester United who only finished in 15th position and failed when the Europa League final.