It is a reasonable question and anytime your not sure you should ask as I would and in my opinion any intelligent person would. ATC are capable of making errors as are pilots.
Having said that I would normally search for differences between the ILS's and if they were minor as they are in this case (different DME) I would have made my own mind up.
The aircraft data base is normally predicated on using a particular DME and that makes the decision easy for you, all though you may not discover the difference until you cross check the altitudes etc. (been there done that more than once)