Not can be slower, but it is actually slower. AMD has by far superior drivers and performance for AAA games released in the last 5 years for R9 280X compared to GTX770. Reviewing GameGPU's data since November 2014, 770 is getting blown out by R9 280X/7970Ghz in many titles.
my post is regarding 770 vs 7950/280, not 280X as I was following the OP options,
and the 770 beats those cards is many new titles as well, so I think can be slower is more realistic.
but if you can get a 280X cheaply and it fits your case/psu decently, why not... one recent problem with old AMD cards is that they likely suffered more 24/7 100% load abuse if it belonged to a miner, but I'm not sure how much of a problem that is... some gamers also like to run their cards for years without cleaning, full of dust and running with some crazy temps.