Im actually glad that you found something to like about XIII. In my opinion, being able to grind up if you are having trouble defeating a boss is literally the point of RPG games. Getting stronger and winning the battles. FFXIII actually restricts you from doing this, its not offering you anything, its taking away opportunity.

Now, onto ffVII. For me, the sidequests begin as soon as you are trying to enter don cornio's mansion. Its upto you what materials you gather and whether or nto you will be picked as Don Cornio's honey. After that theres the optional levels of the shinra building that contain special items and various ways to obtain them. Remember when you had to find the right word? You can just guess, but if you take the time to study the books and get it first go, you will be rewarded with elemental materia, one of the only ones of its kind in game, and its very missable. After that, you have an option to fight midgar zolom, it pass it. Then theres Condor where you can repeatedy return and fight off shinra troops in a mini-game where you hire units and make them fight, failure would result in your team taking out the boss. Sussful attempts will result in an item as a reward and something special late game , all of which is optional. The next I can think of is the gold saucer, theres a ton of mini-games there, then theres chocobo breeding, racing, hidden materia on islands only reachable with certain breeds of chocobo (and a certain one with a pro-highwind pilot) Theres optional characters Vincent and Yuffie, theres a whole sidequest with yuffie (whether you obtain her or not, which I found interesting) Which results in rare materia and more story on Don Cornio, theres optional bosses ruby and emerald weapon. You go from the slums, to distant lands, to beneath the ocean and into space. You pilot giant birds, a massive plane, a submarine, a water-plane and a buggy. You can go back to practically any place you have previously been and find ultimate weapons for your characters. Theres a sleeping man who will give you an item based on how many battles you've fled from and that item can then be given to another man near cosmo canyon for a special item one of which includes a limit break that cannot be obtained otherwise. I dont know if Im missing anything, but FF7 didn't feel linear to me. I was always doing something and there were always optional things to do.

Edit: then there was also the ancient forest where you obtain the apocolypse, one of 2 weapons that has 'triple' growth and theres also rare command and summon materia there. Slash-all and typhoon, I believe. optional