Looking at the Argentine air force, there are 63 outdated fighters, interceptors and ground attack aircraft to replace. These are split over various types that make maintenance extremely expensive and the best course to replace them with something that uses the same airframe and engines for all 60 replacements. The 30 modernized Pucaras are the element best suited to fighting under these conditions and should be modernized and retained.
The JF-17 doesn't appear to be development beyond the A-4 except for some tweaks and it most certainly is in no way a development that outclasses the Tejas despite being in the same price range.
Looking at the history of this programm you see the evident troubles of such weapon imports from China. The European avionics suit was impossible to get and airframe and avionics had to be separated in development. US companies left existing development contracts because of the embargo on China and Russia did join to provide special know-how. All the development was done by the PAC with Chinese help at the costs of 500 million dollars. For the current 50 aircrafts this is 10 million dollars development per airframe. The delivery was second choice because the avionics were not state of the art European nor was the engine that makes this fighter very weak in thrust to weight ratio. The development costs were mostly for a normal light fighter airframe without US cooperation as promised.
I mentioned that before, you can go for China as a military hardware supply source, but then you need a more complete range of deliveries t pay off for the political costs of that move. JF-17 highlights a botched attempt at that as it was not clear to Pakistan what trade-offs they would have to face.
You don't need the Tejas airframe, but it highlights a very important development of reduced number of components by a factor of 90% and light composite construction. That's exactly what can be best maintained under these rough environmental conditions. Same goes for the engine, Gripen made some modifications to the F404 (the standard for light fighters) for simplicity in order to keep it better operational.
Argentina can make a choice: India+Russia (plus Israel) or China (minus Israel) as Russia seems increasingly unlikely to have the same cooperation level with China as with India. Russia alone has a lower cooperation level with Western military technology suppliers than India that due to longstanding and stable political tradition is allowed to combine Russian and Western derived technology. Israel has a US alignment and has been reminded of the implications that limit cooperation with China, especially on US-sensitive issues like fighter avionics.
Complete reliance on Western military supply sources is simply a bad idea for Argentina because they are locked in a conflict with Chile and the UK that can go violent with each and in alliance.
I don't know what complete package China can offer at a bargain price that is about more than fighters. It would most certainly include the next aircraft carrier and amphibious warfare ships/ferries complete with escorts, a range of area denial technology(missiles, surveillance) and the amphibious assault equipment for the ground forces.
Going for India by contrast offers a solution that makes the military supply less hostage/aligned to one partner. As mentioned before, doing business with the Indians is very tricky with lots of well-hidden problems. The best option is to only import know-how and some prototypes. Argentina is on an economic and technological level not inferior to Pakistan or Sweden and I have little doubt that they can modify the air inlets of the Tejas and add good vertical thrust vectoring. It's always been easy to get India and Israel to cooperate on something and Israel is pretty much the top avionics source, except China, for Argentina. The JF-17 and the Tejas offer themselves for a direct comparison of the development of two countries that are almost identical in their problems of making promises that can't be kept and hiding problems. More than twice as much investment went into the Tejas airframe than into the JF-17 airframe with the JF-17 representing a solution of past technology for a light fighter and the Tejas taking the lead into the future. The JF-17 has no carrier component and will need modifications for naval operations unnecessary for Pakistan. Livefist: "LCA Far Ahead Of JF-17 In Contemporary Technology": IAF Western Commander is a blog post with interesting comments on JF-17 and Tejas worth reading.
The true potential of the Tejas needs some more tweaks for the thrust vectoring it is designed for in order to fully outclass the F-16, the other specific design requirement. I'm not sure about the air intakes, but if you look at the HAL Marut(indigenous development by exiled German team) and the HAL Ajeet(license production and development), there might be some established Indian tradition to it that is slowly changing (just like Americans using trapezoidal wings or the Euro-canards).
I have no doubt that China can deliver Argentina something like the Tejas reliable on time at the same costs as the rather dated JF-17 or a weaponized L-15 design that can be shot in droves by the F-16, but what are the political consequences, how will these affect Argentina and what are actual total costs due to repercussions?