[FallingSlowly]

First of all, I think both are perfectly able to empathise and sympathise. I don't particularly like the attempts to latch either on to a specific function, although I can see why Fe is more commonly linked to expressing sympathy (expression = outward), and Fi to feeling empathy (feeling = inward). I think it's much more complicated than that though.

I also don't think that Fe is necessarily more likely to join in laughing, crying etc. It's much more situational than that. I'll try to explain how personally perceive it (might be totally off)...

Fe's reference is the object. That doesn't mean though I will haphazardly join in to whatever emotion someone else is expressing. If someone cries, I am much more likely to evaluate what would make them feel better (and I think that if some "Fe/Ti oscillation" starts in that situation, it can actually even come across "Te-ish" to some people). It's a very conscious process. I simply try to help, be kind and appropriate (of course our perception of "kind and appropriate" can on occasion be perceived out of place, it's not like we're mind-readers or something. I think these flukes are less likely to happen with age/experience though). And trying to understand why they are crying definitely has a part in that, because if I don't, I can't help. Quite simple really.

Blubbering along on the other hand is not something I usually do, it totally impairs judgment in my world. My behaviour of choice could be any of those:

• leaving them alone and retreat
• offering comfort (both silent or through talking)
• trying to make them laugh
• snapping them out of it and kicking their butt
• ...

That doesn't mean that I can't get emotional and cry along on occasion, but I don't perceive that as a Fe trait if I'm honest. It usually happens when something hits too close to home, when the focus actually shifts from outside to inside (myself).
So on that note, I could understand why someone would actually think Fi might be more likely to join in crying than Fe, or that Fi might be related to empathy, whilst Fe detaches itself and seeks to express sympathy. I think however that in the case of Fe, past felt empathy can feed and improve present sympathising - I don't necessarily need to feel strong empathy in the moment to sympathise though, if that makes any sense?
(I probably worded that shittily, but that's how I perceive it.)

I am much more likely to "join in" when positive emotions are expressed, because it has less potential to step on someone's toes, and I also think it makes bonding/opening up easier.

Also, the place in the stacking certainly has an influence. A Fe dom will probably react completely differently compared to someone with inferior Fe. I'd imagine the same applies to Fi.