Fala is a lot closer to the train and bus stations (if you want to catch the Croatia Airlines bus to the airport) than Antunovic, which is out in the west somewhere. In fact it's just about within walking distance of the railway station, although maybe not with luggage. Several buses from the train station go down there too. I don't know what the connections to Antunovic are like.
On the other hand if you do want a gym/pool then the facilities at Antunovic are meant to be very good - depending on when you're travelling, there might be some better deals online - AsiaRooms.com (part of TUI apparently) had rates from 60-80 GBP/night for a single room there when I googled it a while ago, and Expedia started at 67 GBP for a random Saturday night next month. The hotel is geared towards business travellers so there's probably more chance of a better price at the weekend.