If your house was built before 1986 and has a cast iron sewer system, you should NOT replace your toilet with a new one, and you should rebuild the old one if possible. Newer toilets use much less water per flush than older toilets, and this is great for smooth, plastic drain piping - not so much for older cast iron sewer pipes. Because these systems are usually rough and corroded, the large amount of water put down the drain every time an older toilet is flushed helps move all the waste out of the system and prevent more frequent clogs.
If your house was built after 1986 and has a normal PVC sewer piping system, the decision to rebuild or replace really just comes down to an ROI valuation. If the issues with the old toilet will cost more to fix than it is worth to you, it makes more sense to replace it with a new one. If the advantages of a brand-new toilet with a newer, nicer design are not worth the added cost of replacing, it may make more sense to rebuild the old toilet.