Of the deer I shoot enough of to comment on (roe, sika and fallow), I’d say that habitat/food, time of year, age and sex have a much greater effect on taste than species.
I have even started to think that many things we believe important have little to no effect at all.
One of the most revealing meals I’ve had: visiting a friend in Devon in mid summer. Hot and muggy (18-22 degrees at dusk, no wind). Humane despatch call - red stag seen alive but immobile in a roadside ditch, with what turned out to be a smashed pelvis. Unclear how long it’s been there. We went out, and arrived about an hour after the call (so it had to have been there at least an hour and a half). Shot in the head with a shotgun, gralloched and dragged to the car.
Hung up in the garden over night, and carcass stripped the next morning (inside of haunches very obviously still warm). Meat stored wherever it could go. I think most ended up in a freezer, but some went into a fridge, and some may have sat out.
The evening of the day after (as in around 46 hours after a long and traumatic death) we had the fillets (back straps) for dinner.
They were absolutely delicious. Not just edible but so delicious as to cause everyone to fight over who got seconds and thirds. Three families and a semi vegetarian visitor, all with extensive experience eating game, all agreed it was some of the best steak, from any creature, they’d had.
So: (1) a species often regarded as the least tasty; (2) of the less tasty sex; (3) given a hideously protracted and stressful death; (4) butchered in every violation of best practice in the middle of a hot summer; (5) with meat that was not hung or marinated or tenderised or had anything at all done to it other than have heat and salt applied. Despite ALL this still tasted absolutely marvellous.
Meanwhile I have have had sika and fallow that were head shot in winter, gralloched, bled and lardered within a few hours, then hung for a week, and found them challenging enough that the less game-committed gave up, even after the liberal application of bbq sauce.