The Spartans would win against both team iterations (i.e. would win against the team with Batman, as well as against the team with Spiderman).
Why?
Well, you have 7 people going against 300.
Now, the 7 people are all super-amazing .....they are excellent combatants, above par strategists, and can flick a lightswitch with a batarang at 40 paces.
However the team of 300 is also no joke. While NONE of them approach ANY of the other team in pure fighting ability (well, that is actually debatable), the fact still remains that they are good. Very Very Very good at fighting.
Furthermore as Spartans they have been training in combat since they were tots.
Also consider their mental paradigm .....these guys do not believe in defeat. The only way to lose is to die, and the only way to die is if you take as many of the other people with you.
Anyways, what you have here is a situation that actually happens in the wilds of Africa .....the situation when a pride of lions comes against a pack of Hyena.
Now, one Hyena has no chance whatsoever against a lioness (let me use lioness since normlaly there are only one to two lions in a pride, and the rest is lionesses and cubs). One Hyena is dead meat.
This is also the case when you have two hyenas. One lioness will slay two just as easily as it can slay one.
However an issue starts to arise when you have a 3:1 ratio. While the lioness is defending against 2 the third one is free to nip at it from oblique angles, and with a hyena it just takes one good bite and that lioness is seriously injured (immediately degrading its fighting ability, and allowing the others to kill it).
Now, looking at a macro level. A pride of lions versus a pack of Hyena.
Same thing ....less than a 3:1 ratio and the lions will not abandon their kill. More than a 3:1 ratio (e.g. 5 lions against 15+ hyena) and the lions immediately abandon their kill rather than risk injury.
Same thing with the 7 versus 300 situation.
Any of them 7 can take out a Spartan.
Several of the 7 can take out several Spartan solo.
A couple from the 7 (e.g. Spiderman) can take out many Spartans and do it solo.
However in direct combat they cannot take out 300.
Why?
Well, it is called attrition (all combat degradation). Basically, you can kill 50 Spartans and the 250 remaining will still have more or less the same fighting ability that they had when they were 300.
However, kill 2 people out of 7 nd the remaining 5 do not have the same fighting ability.
Numbers matter.
Every Spartan killed will not degrade their fighting ability much until it comes down to less than 100 Spartans.
However, ever member of the 7 that is taken out affects the team.
Kill 3 Spartans and you still have 297 warriors left.
Kill 3 of the team and you only have 4 people left.
It is a definite that the Spartans will kill some of the team (the opposite is also true), and it will reach a point where enough of the team is dead or injured that even Spiderman will fall.
In direct combat, Spartans 10/10.
The only real option that the team has (since there is no immediate prep) would be to escape (which they should be able to do) and take time to come up with a strategy (i.e. prep). Without that, and in a confined space, they really have no chance.
Phillip of Macedon: "You are advised to submit without further delay, for if I bring my army into your land, I will destroy your farms, slay your people, and raze your city".
Whats funny about all this is that it is true (and I would agree, logically it is correct), HOWEVER.....those 300 Spartans? The REALLY famous 300 that fought the 5,283,220* Persians? They proved the rule wrong on the foundation that numbers matter. I still see the 300 hundred winning, but I wanted to point that out.
*Number taken from Wiki and that composed of more than JUST Persians, and yes it was more than JUST the 300 Spartans, but hey they are what mattered