Yes you can use them both, there's no reason you can't.
It may however be difficult. They're both bloom boosters so I wouldn't use them both at the same time. For example, Tiger Bloom probably compares most closely with Advanced Nutrients Big Bud. Now on AN's feeding schedule you stop using Big Bud and switch to Overdrive towards the end of flowering. So if I wanted to use Tiger Bloom and Overdrive on the same grow, that's how I'd do it: I'd stop using Tiger Bloom at the same point AN recommends switching from Big Bud to Overdrive, and start using Overdrive then.
But just for the sake of keeping things easy, I use Big Bud and Overdrive. I find it much simpler to stick with one line of nutes.