I'm asked this question all the time. IF it's only one or the other, and no outside considerations (such as disturbing neighbors, or keeping what you do somewhat private), I'd recommend a power hammer. The learning curve for a power hammer is fairly short. If a hammer banging would start a war with neighbors, then likely a press, although the learning curve is much steeper (and more dangerous) then a hammer.
The reason I say that is...... until an individual gains experience with a press, they tend to wreck a lot of steel, and in many cases "break" the press. Things such as trying to use too much force, not centering the work under the center of force, etc. Most go into owning a press with the idea in their mind that because there is so much force available, they need to use it all. Using a press to it's full advantage isn't about brute force, it's about finesse. Even though I have a press that produces 80 tons of force, that amount of force is there for when I forge BIG billets/cans....... I rarely take a "bite" (compression) of anything more them about 1/4" at a time, and usually less. At the current stage in my career, I personally could not be without either one. I consider the press to be my "precision", and the air hammer to be my "speed". Each has it's own merits, and each does things that the other can't.....at least not nearly as well/smoothly.
I'm not a fan of converting a log splitter, simply because the entire thing was not designed or engineered to withstand the repetitions of force, and the heating/cooling cycles a forging press encounters. ALL the parts on a press need to well maintained! You can often get away with worn parts on a hammer, and not have to be overly concerned about it in comparison to a press. If you let parts of a press get worn, and don't repair them, very bad things can happen. When I read your post about the log splitter being old, the red lights went off in my head. There's just so much more, and so much varied stresses with using a forging press, it's impossible to convey the amount/levels of stress a forging press must endure. That's the reason whenever someone asks me about building a press, I always tell them to design it as heavy duty as they can....then double it.
Not sure whether you're thinking build or buy a hammer, but with the prices of steel these days, check carefully between building and buying. Not long ago a friend was going to build himself an air hammer...... and by the time he figured it all up, he was money ahead driving from Montana to Texas, and picking up an Anyang 33lb hammer.... with his 1/2 ton pickup. Although the price has jumped significantly, thanks to Forged in Fire, there are still 25 and 50lb Little Giant hammers out there for sale..... you'd just have to be willing to go through the logistics of getting it from where you find/buy it, to where you use it.
