Avid had a brilliant idea, but it executed it quite poorly. Pro Tools First was born of a smart marketing plan: get potential customers familiar with their software for free, so they will purchase it when they hit the restrictions, because they are comfortable with the software interface.
PreSonus's Studio One Prime follows the same logic, only with Prime, you are actually getting a full on DAW. And when you finally hit a limitation in Prime, you don't have to go out and buy the full Studio One, all you need to do is purchase a plug in from PreSonus, for that one thing you are missing. In other words with the Studio One route, you go from a 100% free fully functioning DAW (Prime) to spending an amount of your choice, on the select features you really want. In the Pro Tools route you go from a virtually useless learning module* (First) to paying almost $1000 if you wish to upgrade.
One Important Note:
*I don't want you to think I am saying you shouldn't try out Pro Tools First though. Don't forget Avid likes to remind us Pro Tools is the self-proclaimed "industry standard". So since it has a fair sized user base, it's wise to familiarize yourself with how it works.
If you are serious about getting into audio engineering or sound design, I recommend you download First and play with it (you never know, you may get a job in the future that requires you to use Pro Tools). But when it comes to needing a free work horse DAW, go download Studio One Prime.