Always remove anything not specifically mentioned as staying during the trade in talks unless you really don't want it or it's too much work. As others have stated extras don't really mean much to trade in prices, the dealer is buying a make and model and in many cases just shipping the thing off to the auctions to get rid of it.
The guy the dealer rings on the phone to get his "best price" for your trade in is just a local broker who is sitting at his computer checking out things like Redbook and other industry related sites, he's not checking for a model with $10K of extras bolted to it he's checking for a model with a claimed distance and condition the dollars added for the extras usually come down to the dealer themselves as quite often cars going straight to auction get many of the decent extras stripped anyway.
My old man knows the local broker all the dealers around here ring and was speaking to him during money talks when I was first looking at the DMAX, despite the Forrestor having about $4K of extras fitted to it the price he gave the dealer took none of that into account, one because my $4K spend isn't worth that much second hand and two because the extras don't really make a huge difference to the dealer until the car is actually sitting on the lot and he's trying to on sell it with any story he can to some other customer. Interestingly enough the Dmax dealer was the only guy who started out with a trade in price higher than the price the broker gave him and that was only $750 higher so it's not like the $4k of extras was worth much at trade in time.
If a car does have $10K of extras added to it and they aren't that hard to remove the price you can get for them selling private will always be better than the possible price a dealer will give you for the total package, especially since the dealer wont give you a price then say he's adding $10K because the extras are so good. A dealers price is really only going to fluctuate from the brokers price depending on their sales margin for the new car and how much they can make off the extras for the new car which can hide the higher trade in cost