The TT carbon bike is more aerodynamic, and aerodynamics trumps weight, unless you’re climbing at slow speed. If you lose body weight the reality is it will come with increased fitness, so losing a pound of body weight is always better than losing a pound of bike weight. A pound off your bike is dead weight. A pound off your body comes with additional benefits in fitness.
Upgrading bikes and kit is just nice. Full stop. Nothing to do with achieving tangible and noticeable benefits. No need to justify it. If you want it, and can afford it, and get it past your other half, fill yer boots!
The average person is carrying about 70,000 calories of lard, so plenty of poundage to be going at before you start chasing grams off your bike justifying that its better to lose weight off the bike. Unless you’re sub 10% body fat that justification just doesn’t stick!