Against and Towards can be same?
Solution 1:
Against and towards can be used interchangeably in some circumstances, but I don't think this is one of them. In this case, towards would imply affection and against would imply distate or dislike.
An example of a situation where they could be used interchangeably would be "Please apply the overpayment against/towards my existing credit card balance."
As for a rule, I'm not sure there is one. Maybe if emotions are involved, don't use them interchangeably but if there are no feelings involved, then it is ok to do so
Solution 2:
Absolutely you can use both of these sentences to mean the same thing -- if the thing you feel towards that person is antipathy, hate, or some other ugly, negative feeling.
"I feel intense hatred towards her"
"I feel an intense hatred against her."
In this case -- where both sentences are expressing something negative -- the meaning can be the same. "Towards" means "in the direction of", "against" means "in opposition towards". Both express direction, one neutrally and the other pejoratively.
However, the same does not hold for positive, good feelings. One cannot say, for instance, "I feel an intense love against her." This is because "against" is a preposition that describes opposition, and often direct opposition with physical contact. So one could perhaps say "I feel a love, towards her" -- which is a little awkward, but possible -- or one could say "I feel fondness towards her", which would be a little more acceptable. But one couldn't say "I feel fondness against her", because to say that would put the meaning of "love" or "fondness" in conflict with the meaning of "against".