Hi & welcome to the forum!
Firstly, consider why are you feeding what you are? Your first horse needs extra 'groceries' by the sound of it, but not the second. Are you concerned about balancing their nutrition?
Your friend is right that sweet feed is generally 'junk food'. Oats can sometimes be a good & appropriate feed for horses, but they're still high starch & can be problematic, like other cereal grains, but to a lesser degree. They're also not a good source of minerals & vitamins, especially with modern farming & fertilising practices. They're high in phosphorus & can be in potassium, but little else. If that's what's needed to balance a diet, then they may be appropriate. If you can feed them little & often, rather than over only 1-2 larger meals daily, they may be appropriate, otherwise I'd look for alternatives.
Alfalfa is a great feed for horses generally. It's high in many nutrients, especially calcium & protein. It's also high energy, so good for horses that need extra calories, but needs to be fed sparingly if at all to 'easy keepers'. Beet pulp is also high energy, high Ca & other nutrients. It's high fibre too, so a good feed, but again be careful with energy levels for easy keepers.
As for how much to feed them, the first horse needs more & as the second is overweight, it only needs a small amount of low calorie whatever, enough to provide good nutrition. As for what you might feed, that depends on what they're getting out of their pasture for a start, nutrition-wise, and while your thin horse needs some high energy feed to gain weight, such as alfalfa, beet pulp, etc, this should be fed sparingly if at all to the fatty.
It's also important to change/add feed gradually. While you may want to get up to the amount suggested by your friend(need weights of feed, scoops don't tell how much) for the horse than needs extra, I'd start with something like a cup(1/4lb) of each(measure beet pulp dry) & build up gradually over a week or 2.
So.... I'd ditch the sweets, but keep the alfalfa & possibly add some beet pulp to the first horse's ration. I'd give the second horse no more than about a handful of alfalfa or beet, to be a carrier for whatever nutritional supplement is appropriate, which may or may not include oats. As for working out what they're getting from their diet & what may need supping, FeedXL Horse Nutrition: The D.I.Y. equine diet planner
is one great resource for that.