ZFR: So, I can answer the first question at least. The levels and story are exactly same, you get slightly different cutscenes of course to show that you play with Jack instead of Jos.
As for the second question. I gave it a go with the following rule: bless your weakest axe and buy the cheapest silver one, but no other axes. Don't upgrade any hand-to-hand, health or stamina skills. Don't use any damage reductionitems. When playing don't use the axe, unless you must. It was fun. The will-o-wisps were the worst, because it was almost impossible not to go mellee with them (you could use wayside corss to help you, but you could rarely rely on having them take out will-o-wisps without mellee because you had to time the prayers just right). Andf you couldn't use guns because will-o-wisps had ranged attacks. I drank beer (temporarily no fatigue) to help me with those fights. Other than that mostly relied on traps, guns and fear factor (e.g. bonfires were much more useful than in first game). Final fight was a bit tough, but I bought lots of drinks for it.
You had less money, because you spent more on traps and bullets, but then again I didn't need as much items (no axes) and drinks are cheap.
Made you rethink your strategies. If you enjoyed playing with Jos, give Jack a go.
Thanks for bringing this out. I had the same question myself.
Starting with Jack is really hard. So I confess I had to go back to Jos and wield an axe in order to fit the shortcomings of my strategy and execution. It feels that it must be like you say: playing with Jack makes for a very different game. Worth a replay!
Also, the savegame system with no savegames, just allowing you to go back in time, should you be cajoled because of bad purchases or unexpected challenges, is superb. AFAIK it was first implemented by the adventure game The Last Express. Good to have games that dare doing things differently. Cheers.