I bought a Rem 783 in .243 a couple of years ago when the package deals were scope and rifle for $549. The Axis was slightly dearer, I went with the 783, felt all along that I should have gone the Axis. Sold the 783 at a profit when the price of the packages went up and bought myself a Tikka with some cash I had put away.
The 783 was accurate, and light, and felt nice to handle. The bolt throw is long and the bolt head being flat was annoying, and would always sit closer to my scope than I was happy with (difficult to reload quickly). At the time extended aftermarket mags were not available, however you can get them now. Having moulded points for mounting slings was always something that bugged me - if you want to fit a bipod you are best off cutting them off and drilling a hole to glue a sling swivel in.
The turning point for me was when I came across a mob of goats and was fumbling with the bolt because I was not accustomed to the length of throw / how far the bolt head came up / the odd shape of it. Certainly not that big an issue in the scheme of things but it just bugged me.
Trigger was very nice though.
Honestly, for the money, and I say this as someone who bought a Tikka, buy the Howa package. Way more aftermarket options for the Howa than the 783 or the Axis, much better value for money. Hope this has helped