Couple of points on this one...
Would Argentine have moved to an all professional Army without the humiliating defeat of the 1982 war? OTL they only did this in 1995 and 5 years isn't enough to rebuild and create a decent army.
I think so. While the defeat in '82 discredited the armed forces and exposed quite a lot of failures which wouldn't show up without it, Menem decided to end conscription over the scandal of a conscript killed by his superior officers/NCOs, plus he wanted to cut down the army's manpower and it increased his public image.
I think a similar scandal might very well happen anyway and while (hopefully) Menem's presidency could be butterflied away, there is the question of how much money would the following democratic governments willing to invest in the armed forces.
So while Britain would have less available assets for a task force, Argentina might not have armed forces that different from those of 1982. At the very best, I could see upgraded fighters but probably nothing in the level of an F-16, just maybe four modern electric subs (which, with proper recon to locate ships, might be a huge danger to British warships) plus the full compliment of exocets and Super Etandards. No carrier, as it's likely to break up eventually as in OTL and funds won't be granted to replace it. Every failure in the Argentine officer corps is likely to remain, although there might a few more 'elite' units: fully professionalized and properly led.
The other difference is that any politician is going to plan such a war properly and not hope everything goes the way he wants.
Still, there is the issue of potential American or French involvement.
EDIT: regarding exocets, they would have proven their value in the Iraq-Iran war, so British ships might already have some sort of CIWS mounted by 2000