You could say:

J’ai aussi peur que vous.

or:

J’ai peur autant que vous.

J’ai autant peur que vous.

But

J’ai autant de peur que vous.

doesn’t quite work for me.

"Quantification of fear" might not quite work with "peur". You can say:

J’ai autant de soucis que vous.

But that is not "fear" anymore, it’s much milder ("worries").

Je suis aussi effrayé que vous.

Could work.

Even if the English read I have as many fears as you do, I don’t think peur is quantifiable in the same way in French. Quoique, you could say:

J’ai autant de peurs que vous.

(plural). It would be grammatical correct, but maybe not very common.