Replace a UPS battery or buy a new UPS?
Solution 1:
I've never heard about replacing a battery causing the UPS to never be the same. The only UPS units that I've ever seen are just sealed lead acid batteries that wouldn't cause issues with the UPS electronics unless they weren't specced right (proper voltage and amperage rating). I've used APC and third party batteries and had luck with both. The third party batteries are generally cheaper so that is the way I would go. You don't need to replace the UPS unless there is something inherently wrong with the UPS electronics.
Solution 2:
I would say that it's definately worth buying a replacement battery. Not to mention is probably better on our environment if you're only changing the battery and not the entire unit.