Any reputation gaining difference is there to give perfect answer for a new question and for a unanswered very old question?
I would say it depends upon which SE site you're considering to answer old questions. For sites having extreme amount of active questions, it is probable that your answer would be missed from "active" tab (first 50 questions) in no time, and most likely would be seen by users reviewing answer's queues, and they being reviewers possibly would scrutinize your answer carefully, so I wouldn't bet here.
If you're considering an old but Beta site with low amount amount of active questions, then you may receive some attention (reputation) from active or casual users, provided that the answer itself is worth (there are exceptions where some users up-vote just anything).
There are other possibilities, but I assume you would have gotten the idea by now.
However, as Shadow Wizard mentioned, if the objective is primarily to receive points by answering questions, then you're simply doing it wrong, because it may lead you to attempt unethical means to gain reputation as well.
For an encouragement (if it can be), you may take a look at my list of answers where the ones under the newest are mostly on old questions, and haven't and possibly won't receive any points or attention at all.
Does that discourage me at all? Of course no!
Did I answer them considering some good points in my mind? Nope! I answered them solely because I wanted to impart my knowledge onto a system I could reply upon that it would take care of it for a long time, and it makes my happy :) Not to mention, I only touched those topics where I'm most comfortable, so I'm confident that I've added quality content irrespective of how it would be received in terms of points.
Anyhow, since one might be tempted to gain those +10, +15 green colored nice and sweet notifications, I would say go with new questions only, until you realize why should you continue with the community.
No, there is no difference, and why would it? Being old doesn't mean it is a high-quality question or it was difficult to answer.
A decent answer will gain up-votes, whether it is posted to an old question or a new one. The new answer will bump the question to the front page so people can review it and vote on it as they wish.
If the question was very hard and someone wanted it to be answered, he/she could have put a bounty on the question, which might be awarded to the late answer.
You are asking the wrong question, in my opinion.
The question should be "Do you care if you will get less reputation from answering an old question?"
And if the answer is "Yes", then you are answering from the wrong reason to begin with.
The reputation should be a bonus, not the main motivation behind answering. (and asking)
But to answer your question, from my personal experience the answer is "yes, this is possible but chances are that you will get more reputation from answering only new questions".
When answering old questions the answers may well disappear without much trace but one extra bit of information you do have is view count.
From the point of view of both reputation and focussing your efforts where they will be most useful to other people this is good info to know.
On StackOverflow 3/5 of my current top answers (all scoring 300+ now) were to highly viewed questions where the existing answers left a gap.