I've been through multiple Astro variants and TB headsets over the years, I don't think you'll be extremely happy with either, long term.
Is $250 your total cap for everything? I can't really comment on the G6 itself but lets assume that's a pretty good option.
For ease of setup, minimal cabling, etc I'd recommend Senn PC37x + G6
For pure performance in a "competitive setting" I'd recommend AD900x +G6+Modmic.
After Infinity Ward fell apart I kind of lost interest in competitive console play (I never really gave Titan Fall the focus it likely deserved), but my favorite setup at the time was with the AT-AD700 with a custom mic attached (antlion was around, but the modmic was not an extremely popular option at the time, nor was it as good as the product they sell now) with a mixamp and DH enabled. It's a bit simpler on pc as I use a desk mic and whatever cans I have within reach, less cable management worry and dac/amp already on hand to power whatever I need. After the ps3/360 generation and the inclusion of TRRS on the controller I "downsized" to a Senn PC360 G4ME (this has been like 7 years now since I bought this headset) and even used it for PC play with a basic Fiio D5 and it still easily outperformed any Astro/TB combo I ever tried. I'd be using that today but I had some projects that required higher fidelity with my Mic setup and moved to a desk mic on a boom.