There much to differ them, first and most noticable would be that Stellaris is realtime.
The only experience i have with MoO is what ive seen read and heard, never played them, but I think Stellaris and MoO sounds very different from eachother.
As it stands right now, id say Stellaris is innovating the genre a great deal.
Real time is not the only key difference, as the whole dynamic is different.
Wars are for goals, not juts painting the m,ap your colour, you need to secure you objectives then occupy, and use orbital bombardment and combat to bring the opponent to the negotiation table.
War goals can be about creating new factions that are aligned to your own regime's so why you can then ally with and help them absorb the old Empire.
Basically installing friendly regimes on your boarders.
So war is more than just conquering a new system, adding it to the pile.
With the way large weapons, and small ships work, Corvettes are not obsoleted by bigger ships as unescorted battleships with All big guns, can be overwhelmed by a on paper weaker force of corvettes due to the evasion of the small ships vs the tracking speed so to speak of the bigger guns.
You can with the right set up fleets with fast corvettes that get close to get into a knife fight, to tie up the enemy, while destroyers put up point defence and shoot at the Corvettes and the Cruisers and battleships hang back and engage at long range.
Creating multiple ship designed for different roles in the same size class is encourage.
In my Current single player game
It is 2365, 165 years in and I have not fought a single war, nor did I have to yet have been well involved in the game of galactic politics
My Empire has 35 Planets and 382 Pops over 13 species, all gained peacefully though uplifting, Enlighten and integrated or migrated in.
The one pre sentient species I uplifted was further genetically modified to be my ground troops, due to their pre existing natural disposition.
A particular Xenophobic race that I Enlightened and had difficulty integrating was Genetically modified to be more... compliant.... and conform better with the Ethos of my ruling state.
It was been an interesting balance of open migration policies, vs the ethics divergence and internal struggle so many races generate, but with so many species I can colonise more of the world types within my boarders.
Humans started the game as pre space faring and reach the FTL level in game becoming an empire, (Well the Human Interplanetary republic) and through trade I now have more humans in my empire than there are in the Human Interplanetary republic
There is an even chain going on, on another world I have been Observing where one of my Scientist when off the deep end and took modern weaponry to the Late Medieval Age Primitives and is currently conquering it, and I have to weight up the lasting effect of direct intervention.
I could go on but Spoilers abound
A very engaging game in a play style of EU IV for when you need it, with the wonderful paradox dynamic event chains to keep the galaxy feeling alive and lived in.
A complete different experience to MOO layered with the familiar 4x gameplay found in MOO