persona - the best rpg games of all times :)

Their spreading the love, which I think is great.

Is there any differences in game-mechanics between SMT, Persona and Persona Golden?

I like Fire Emblem - what are the similarities and differences between FE and Persona/SMT? I do not really understand how these two series could be merged into one game. When I have tried out SMT, it seems to me to be a lot of dialogue between short bursts of FE style fights (with ghost instead of weapons) in 21:st century settings.

Persona 4: The Golden just has extra content compared Persona 4 so there's no meaningful difference in mechanics. The difference between SMT and more recent Persona games is the social simulation elements ... 

Fire Emblem and Persona or SMT are almost ENTIRELY dissimilar other than the fact that they're JRPGs. If anything Fire Emblem has more in common with Final Fantasy Tactics ...

It's a jrpg where you level up yourself and your personas to fight monsters in a dungeon-crawler. Your character has several personas that you pick from while the other characters have 1.
You get personas by fusing the ones you find into higher and higher level ones. The personas are based off the tarot card arcana like strength, devil, angel, queen, princess, etc.
THat's the fighting portion.
Then there's somewhat of a dating sim portion of the game where you go and hang out with people. I think there are either 12 or 20, I can't remember, but you level up those arcana through these social links (s-link). This gives your persona of that arcana better abilities and fusing power, and if you have the corresponding persona on you when you socialize, then that boosts your social power. So the two parts of the game influence each other.
It's about using the right personas to do the right job (like elemental counters) and the right responses to the social interactions.

Plus the story is awesome and the characters are very unique and fun, and great music/presentation.

If they are dissimilar what will be the result of FE x SMT? Fire Emblem Awakening has this bonding-friendship-marriage element. Is it more of that in Persona?

yes it's similar, but also dissimilar.

Social links in persona are based off answering questions. Somebody will say "I don't eat that much nowadays", and you'll have several response like "sounds pretty bad", "why don't you come over and I'll cook", or "you should take more care of yourself". ANd then based on their personality, you'll get 1,2, or 3 stars. There are about 3 questions in every social encounter, so 9 is optimal. Having their arcana persona equipped gives an extra 3 right away, so even if you fail, you still get about average stars. That in turn decides your rank.

In FE, all you have to do is have someone with an affinity toward that person fight next to them in combat.

I like both systems. But yeah, they're distinct but similar. ALso, persona has a love aspect too once you max out the s-link, they become your girlfriend etc.

I personally don't know since we haven't seen any gameplay of SMT x FE ...

Persona is indeed much more aggressive on the whole social gameplay aspect than Fire Emblem will ever be. 

Coming from Fire Emblem, what SMT/Persona game should be the easiest to start with?

You can start from any entry since Persona games pose not a whole lot of difficulty compared to say SMT Digital Devil Saga or mainline SMT games such as Nocturne ...