I think a more fair comparison would be t97 with carry handle vs t81.
If I can only pick one it will be t97 without doubt.
Most importantly T97 accepts 10 round AR pistol mags (with minor hand fitting of mag well). So if I want to do action shooting competition I'm not handicapped by 5 rounds. T97 also has better sight (aperture vs open on t81), is more accurate (2-3 moa vs 4-5 moa on t81), accepts muzzle brake more easily, and way more compact for getting in/out of vehicle. 223 is also softer shooting and lighter to carry than 7.62x39. If you ever shoot at range or competition where anything sticks to magnet is not allowed, 223 is significantly cheaper. Even compare to the cheapest 7.62x39 surplus, decent quality 223 can be had for only about 15 cents more. Not to mention 223 is way cheaper to reload.
Control ergonomics is a toss between the two. T81 does have the advantage of working without fiddling from the factory. But if I want a functional rifle that spew out 7.62x39, it'll be SKS anytime. T81 does not offer anything better than SKS other than the look. Is the AK like look woth $800 to you? (especially you mention the budget only calls for one rifle).