While we love Harry for his quotes and for being the maverick who doesn't follow the "rules" or accepted reason, and still gets the badguys in the end, Harry wasn't a "gun guy".
Now, perhaps he learned a thing or two over the years, but knowing Harry, it would only be the things he wanted to learn...
He carried the .44 mag S&W because it was the biggest, most powerful thing he could get. And sometimes the biggest, most powerful thing you can get is really not the best choice.
Harry's choice for a countersniper rifle in the original film was a .458 Win Mag. Scorpio actually escapes because of the recoil of the .458 keeping Harry from a fast second & third shot.
Today, unless there was some other plot twist added in, Harry would have probably put the Auto Mag back in the box, when he was able to replace it with another S&W .44 Mag. Not a real gun guy, but definitely a revolver guy, by choice. And I seriously doubt he would get one with a built in lock!
NO GLOCK, ever.