Grammatically, there is no problem with either.
But the meaning is unclear in either case.
There are two meanings for "alternate" and "alternative":
- X then Y then X then Y ....
- choosing X or Y
I, like many people, use "alternate" for meaning 1, and "alternative" for meaning 2; but some people use them the other way round, or do not make a consistent difference.
Combining them with "equally": meaning 1 makes no sense at all. Meaning 2 makes a sort of sense, if you mean something like "choosing X or Y, and they are equally attractive choices", but the meaning is very unclear, and I wouldn't advise saying it.
But I don't think that is what you intend either. I'm not clear enough what you do mean to make an alternative (!) suggestion.