It is important to know the difference between these fabrics. If the pattern calls for sewing 'over two' on linen, you can get the same size of project by sewing 'over one' on Aida. However, there are limitations on this change-over. If the linen calls for 'over one', you would have to sew over a half on Aida - i.e. put the needle through the stands of fabric between the holes instead of through the holes. It can be done.
Many people do it.
But, it is up to you if you want to try it. Some designs say that it may not be sewn on Aida. If the linen was 32 count, you need a 16 count of Aida to get the same size picture. If the linen is to be sewn over one, you would have the greatest difficulty in transferring it to Aida, unless you want to sew it over one also, and then the size would come out as twice the original size. It is the greatest pity when a great project gets a black mark.