These are totally different cars, I owned a new wagon r (2015) and upgraded to swift (2017). Here are my two cents:
1) Drive: Swift is a clear winner in comfort, stability, superior braking, acceleration etc. Wagon r well not bad, but is far behind in engine power and braking, although drive ease and spacious cabin is a plus.
2) Fuel Consumption: Wagon R wins by a mile, 12.5-14kmpl with A.C. and 14-17kmpl without A.C. on my driving style, Swift gives 10-12kmpl with A.C. and 12-13.5kmpl without A.C. If you floor a swift fuel consumption will drip to 7-8kmpl. WagonR well is just meant for economy.
3) Transfer/Tax/Token: In Punjab Wagon R would be a lifetime token in 10k, and registration cost would be 25k. Swift transfer would be around that much but in Punjab it's token is 8k for filer and 15k nonfiler every year. If u have to buy Swift then buy an Islamabad registered one.
4) Practicality, Wagon R is the home use car, with more cabin space, more spaces to store stuff and doesn't touch speed breakers with 5 ppl. Swift space is very limited, campy back seat, and it is quite shallow with even 4 ppl sitting in the car.
5) maintenance: this aspects is comparable in both, but generally swift parts/accessories are more expensive being a superior trim.
My verdict is that if u want an economy office going car which u want to put in home use for groceries,go for the new wagon R. If u want driving pleasure and superior braking and don't bother about costs of maintenance/tax/fuel go for Swift.