Probably Tiger Woods 03.
It has alot of courses and players to unlock and full PGA license
A new swing system makes for a very short learning curve but a kind of career mode where you win money and buy attributes to raise your skills as you go.All aspects of the game(chipping, putting etc) are very playable.There is no awkwardness.Power boost and spin control.Fading and hooking is also "natural" in feel.No 3 click swing
50 scenarios where you try to acheive bronze,silver or gold medals.Special challenges award trophy balls like 1st ace,1st 350+ drive.
Tiger challenge where you compete against a variety of players and PGA pros over a bunch of courses.Kinduva a ladder type thing where you play your way up unlocking players and courses as you go.
You actually play to gain 100% completion like in some games llike GTA3.
Online play(will be much better in 04).Monthly suscription rates after free introductory period at EA Sports Online however.
Course editor if you are into that stuff and lots of courses and whatnot available for d/l
Excellent graphics and great sound effects.Lots of stats

Lots of pros like Tiger,Monty,VJ,Leonard etc.
Not very realistic scores as in most golf games.Current lead in console "online" tournament is 43 -29
Not really worth mentioning Links.Just awful in comparison.You have Jack so you know.Links is worse than that.
04 is gonna be a big step up.There will be a 52 week Tournament schedule career mode