I personally find Umbreon to be better overall. Why? Because it has good defensive stats in all three sections (HP/Defense/Special Defense).
While Blissey has amazing special defense and enormous HP, one strong physical move will OHKO it no problem. Umbreon, however, can survive just about any hit, physical or special. It can be very difficult to knock out an Umbreon.
Here is a gen 4 set for Umbreon:
[email protected] Berry/Leftovers
Nature: Relaxed (+Def -Speed)
EVs: 252 HP, 252 Special Defense, 4 Defense
Curse (You'll be slower, but Umbreon isn't known to be fast, so it doesn't matter. Raises Defense and Attack.)
Taunt (prevent the foe from giving you status/setting up)
Payback (you'll always be slower, so this move doubles in power when you're hit first. STAB.)
Yawn/Toxic (Force switches for further setting up curses, or badly poison the foe)
With this set, you'll want to be careful of Steel types. They can wall this set no problem. Umbreon can't learn much to hit those outside dig, which isn't a good move to use competitively.
Hope I helped!