What are your daughters goals, and which horse will be the best to meet them. With the lease its a set time frame and you get to give the horse back right as the contract finishes. With buying, you get to choose the time frame, but when it comes time to buying its not always easy to get a sale right away. It comes down to which horse best suits your daughters level and needs at this time now, and thinking towards the future where your daughter wants to be. If the TB is a horse she can grow on for a couple years that may be the best option since you don't have to worry about giving the horse back on a certain date. If you are looking for a stepping stone and think in 6 months or a year your daughter will need to move on from the 20yr then the lease might be a good option. Honestly, I think the most important thing is which horse works best with your daughter right now. Also, another side note about the lease, not applying to month to month leases, but if your in a year contract, and say after 3 months the horse isn't working, the owner might not take the horse back until the year is over and then your stuck with the horse for another 9 months, I ran into that problem once.