Can a Hermetic magus tell the difference between another magus casting formulaic magic and him casting spontaneous magic? If yes, does he do so automatically (because formulaic magic is far more refined, or takes longer), or does it depend on a roll?
I believe that the published material is silent on this issue.
There is however the perception + awareness roll of ease factor (15-magnitude) to determine the technique and form of a spell being cast. I think spont vs formulaic would be easier. I'd make the ease factor 9 - magnitude
Whatever you set the Ease Factor to, one idea to consider is adding the caster's Finesse to it.
The idea being, for somewhat without much finesse, a spell made up on the spot is going to look so much sloppier than a formulaic spell he's practiced a thousand times. On the other hand, for someone with amazing talent at graceful and precise spellcasting, it might be hard to recognize that a spell isn't formulaic.
If you are doing that, maximum of 15 then. It should not be harder to recognize a spont than formulaic.
Er. We're talking the difficulty here of recognizing whether a spell is spontaneous or not.
This is entirely separate from the 15-difficulty of recognizing the technique and form of a spell. That difficulty 15 is true regardless of whether the spell you're looking at is spontaneous or formulaic, and was only used as a basis for comparison by one of the other posters. It's not really directly related.
There's no reason someone with impossibly high finesse couldn't near-perfectly (say, difficulty 17 to notice) disguise his spontaneous spells as formulaic spells. Even if it was difficulty 20+ to recognize whether a spont, the difficulty would still be 15 to recognize what arts were involved, anyway.
I disagree. Spontaneous magic is sloppy, imperfect, and inferior to Formulaic magic. Easy to spot, almost automatic. I would say it is an ease factor of only 3 - magnitude to recognize, and Finesse would add only +1 for every three points.
, just fanning the flames...
Don't forget we have two kinds of spontaneous spell casting. "On the fly" and "ritual". I'm thinking it would be easy to notice the first, not so easy the second.
I am going to ask a question that might be totally irrelevant but how does it matter?
The person watching automatically sees it is hermetic magic. They can with a roll determine technique+form. Does it matter if it is a level 15 spont or a level 15 formulaic: They have the same effect guidelines, same range, duration and target limitations and when they take effect, the effects are indistinguishable from each other. They both can be fast cast (spont naturally, formulaic by mastering with fast casting). Both may or may not tire caster.
Is there a practical reason to know if it is spontaneous or not?
Well, If I see someone cast a 8th magnitude formulaic spell, that's not too scary. If I see someone spon. a 8th magnitude effect, it's bootlicking time.....
A Flambeau magus never lick boots. Stand and die, but never submit
Life linked Spontaneous magic can do wonders 
Especially when combined with Diedne Magic 
Which is a good reason to want to detect who is casting what kind of spell.
But isn't this scrying?
Guess that makes them an endangered species then.
Nope. Make the ones who demand submission the endangered species.
This is the main reason for this question: I have a Verditius magus with Diedne Magic in my group, who'd like to know if the difference can be noticed, since he's afraid his lineage might be discovered if he overindulges in spontaneous magic, since Verditius magi aren't particularly known for their skill in the latter.
It might be much easier to tell with a Verditious, because the character isn't really using a casting tool (even though they could certainly hold something that looked like one).
Enchant Casting Tools and Bind Magical Creatures (House mysteries for him) are something he should seek out quickly. Get a reputation for doing things you can't do with Hermetic magic (Magical and Faerie creatures can have powers that don't follow the Limits!) and people will fill in the blank themselves. Hide in plain sight.
I think my default assumption is that a magi would know if something was spont or formulaic just by looking. No roll required.