Is your current air purifier true HEPA? If it is, you need to change both the filters periodically, and with birds in the house it's helpful to vacuum the prefilter occasionally to get the dust and dander off. Replacing the filters is a lot cheaper than replacing the whole air purifier. It's easy to order filters online, and your local Home Depot might have the right size on the shelves.
With the new purifier that you suggested, the true HEPA part sounds great. But I don't know about the UV-C and the titanium dioxide because I've never researched these things. UVC is damaging radiation, and I'd want to know EXACTLY what they're doing with it. Even if it's contained within the purifier, I think I'd feel more comfortable letting the germs live than blasting UVC at them. The listing on Amazon says "UV-C light sanitizes by permanently damaging the DNA of germs so they die." I'd be worried about it damaging the DNA of birds and people if it gets out into the room, or of damaging the DNA of germs so it mutates into something REALLY nasty instead of dying.
This scientific paper says titanium dioxide nanoparticles are possibly carcinogenic and should be used with caution until we know more about them:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3423755/ I don't know whether this air purifier emits these particles, but I'd want to find out before I used this feature in an air purifier. Plain simple true HEPA is all that you really need, but it's getting harder to find air purifiers that haven't been jazzed up with a bunch of additional features.