Comparisons using "different" with noun phrases

Fallow deer have different antlers from red deers.

I am struggling to find a better way to form this sentence. I cannot tell if it is correct or sounds natural to a native speaker.

A small reordering of the elements in the phrase seems to help:

Fallow deer have antlers different from red deers.

Yet, I am still in the dark as to whether the first option is acceptable.

I guess I may be struggling with this sentence because deer is the non-genitive plural, deers the genitive plural and I want to convey that the antlers are different, not that the fallow deer antlers are different from the animal that is the red deer.

I would appreciate your input on the sentences proposed above and ask what an informal way to convey the same meaning would be.

I wouldn't use either of your two examples. Compound nouns like red deer antlers don't need the possessive form deer's. In fact, I find it weird. I don't think its necessarily wrong, but it's not idiomatic here in the UK at least. Note also that deer is both the singular and plural form, and deer's is both the singular and plural possessive form.

I would only use the possessive form if I was talking about specific antlers belonging to one or more specific deer: e.g. We removed the red deer's antlers.

Anyway, there are several possibilities (possibly more), as I see it:

Fallow deer antlers are different from red deer antlers.

Fallow deer antlers are different from [those of] red deer.

Fallow deer have different antlers from [those of] red deer.

Fallow deer have antlers [that are] different from [those of] red deer

Fallow deer antlers differ from [those of] red deer.

Fallow [deer antlers] and red deer antlers are different.

Fallow [deer] and red deer have different antlers.

Fallow [deer antlers] and red deer antlers differ.

Note: The words in square brackets can be elided in informal English, because they are obvious.

Personally, I'd go for the shortest ones.

Fallow and red deer antlers differ/are different