I’ve not heard of too many people doing a through-hike from Jasper to Banff, except for a few continental divide hikers. If you’re interested in such an adventure there’s a book by Dustin Lynx called ‘Hiking Canada’s great divide trail’. The sections that goes through Banff would probably take 10 -20 days or so alone (Assiniboine to Field)… It would be quite interesting and leave you with options for re-supply etc. I don’t know about how it would be to hike the rest of the way to Jasper, but anything is possible! Hiking the other direction south from Kananaskis-country to the border is not as interesting, cuz you would have to go through a number of non-park areas that are not protected and have forestry and mining activity.
I've got both books that Selkie has suggested and the Copeland guide is your best bet, despite the pretentiousness of the title! When you say "Banff and Jasper" you should keep in mind the other bordering mountain parks (Assiniboine, Yoho, Kootenay, Kananaskis/Peter Lougheed, Robson etc.) These are covered in both guidebooks.
Because these parks are so big your map is probably some ridiculous scale. I have a number of gov't topo's at 1:50,000 that I bought at the local scout shop but each one individually only covers a small area, you'd probably need to buy a couple dozen to cover Banff and Jasper... Cuz the maps are so expensive I'd just get them for the specific areas you are hiking. You can get gov't topos from Gem trek maps or Go trekker maps, maybe also from
www.mec.ca
I've backpacked a bit in the Skoki region of Banff as well as Kootenay park (the Rockwall) both are awesome areas. Assiniboine Park is really cool too. Can’t go wrong but you will have to reserve your back country campsites asap.