Do you like Cadillacs or Pontiacs?
Budget considerations in a rifle purchase?
Do you want to buy once, buy right, or do you want to just get your feet wet with little outlay and see if this is for you?
The Model 700 is their top of the line action, which has been around for over 65 years. The one most copied and most used for custom rifle builds.(45ACPKING; nice build! The 338 Federal is a great cartridge!) As previously mentioned, do not let bad press initiated by those against riflesin general be a deterrent.
The Model 783 is their budget priced entry level rifle made to meet the demand to be sold in box stores. Apparently has been getting good reviews here.
While I do not have a deep wallet, I am a lefty, with a propensity for cartridges that are not run-of-the-mill. This means that I usually have to have a custom rifle built toget what I am looking for. The Remington 700 has been the go to platform for most of my builds. Yes, I have used other manufacturers as well (Sako and Ruger), but the Remington is usually easier to acquire left handed, and has the most options available for extra goodies (as previously mentioned). No, I do not own a 783, nor am I about to...but that is just me.
To the poster looking for a budget left handed rifle; The Ruger American is available for those of us in our "right minds". My uncle's rifle, which I set up a scope on for him, and broke it in, will print sub-MOA groups with Federal blue box ammo consistently.