So my answer is largely from Karl Marlantes' 'What it's like to go to war', which covers a lot of the philosophy behind war, including why society sends younger men instead of old. (I very much recommend this book as a side note, it definitely gives a lot of useful insights to this topic)
One of the main advantages, at least tn Marlantes' view, is that young adults (men primarily) are psychologically better suited to fight a war. Sending off someone to fight and potentially kill people they've never met is difficult, and young men have certain advantages.
Young men, being full of hormones, are significantly easier to train to do this as it's easier to instill an 'us vs them' mentality, group loyalty, and a disdain for the enemy without having met them. Being able to tap in to controlled aggression as a 19 year old is a significant advantage from a soldiering perspective when in combat, as it makes men more willing to advance in combat. Once a man reaches 25 or so, he's less hormonal and has reached more of a level of emotional maturity and is more likely to question why he's fighting and killing these people who probably aren't very different from him.
One of the biggest psychological aspects is probably that younger people have a reduced sense of mortality- they often (sometimes subconsciously) justify death as something that isn't going to happen to them, whereas a 25 year old may still think of everything he has to live for in a battle and be more hesitant to do his job.
Finally, it's a lot easier to mold a 16 or 18 year old, compared to a 25 year old. You need to break a person down and build them back up in order to become an effective soldier- once they are 25 or so they've already developed a strong sense of individual identity so this is much harder.
One counterpoint is that this viewpoint lies in exploiting the immaturity of 16-19 year olds. The role of a special forces operative is definitely different to that of a traditional soldier, and is better suited to people who are a bit older, more independent and more mature. So it comes down to whether you want your supersoldiers to be mainly really effective infantry (think Spartans from HALO), or real life special forces like Green Berets who have to use a lot more independence in how they approach a task.
On top of this, you have the physical aspect. While a 16 year old may not be as strong as a 25 year old, their body is much better suited to recovery, and after all fighting a war exacts a pretty big physical toll on people. Being able to recover quickly after a long march or battle or carry kit for extended periods makes them a lot more effective.