Appeal is the power of attracting or arousing interest.
In this sence an attraction is something that attracts interest.
They are not synonyms.
In the case above, we can use both, but only one gives the desired meaning: Sweet desserts don't have any appealfor me.
This means that the desserts aren't appealing to you. Sweet desserts don't have any attraction to me.
This means that the desserts aren't attracted to you. This isn't surprising really, unless you have a superpower that magnetises desserts.
Thanks, Niall, for the beneficial analysis.
I still have some doubts, though.
First, why is it wrong to write "Sweet desserts don't have any appeal to me?"
Second, should I use in or with in "Do both appeal and attraction work with/in the above wording?
To answer your second question first (because it is easiest), both with and in work equally well in your sentence.
As for your first question:
We don't tend to use the preposition to in this case, whether that means it is wrong is a different matter.
We would usually say Sweet desserts don't appeal to me. or For me, sweet desserts have no appeal.
As in my first example there, we have two phrases which mean are appealing and they are:
- to appeal to (person or pronoun)
- to have appeal for (person or pronoun)
Also, as an aside, we use appeal to in another circumstance. I appeal to him means I ask something of him or I ask him something.
This is used more in spoken English and isn't very formal.