Pathfinder Unchained describes how the Unchained Summoner differs from the original.
Most of the summoner’s class features are the same as those of the class’s original design—the biggest change comes to the eidolon. The unchained summoner selects a subtype for his eidolon (such as angel, demon, or protean), which determines a number of its evolutions and helps to shape the eidolon’s general attitude and appearance. In addition, some of the evolutions are now tied to one or more subtypes and base forms, to make eidolons that better match the expected appearances and abilities of such creatures. Finally, the summoner spell list has been greatly revised, removing a number of imbalances.
Change 1. Eidolon subtypes and limited evolutions
If you compare the per-level progression of the APG (Advanced Players Guide) eidolon and unchained eidolon, you may notice that the evolution points per level has been reduced. The per-level BAB, HD, skills, feats, and other progressions are unchanged.
For the APG eidolon, customization involves a base form (chosen at 1st level), plus many evolution points allocated into evolutions. Some evolutions are restricted to certain base forms. Since evolution points can be re-spent at each level, this gives the APG Summoner flexibility in advancing the eidolon, and often encourages builds that optimize melee damage via natural attacks. With some optimization, the APG eidolon can outshine other martial characters in the party.
In contrast, much of the Unchained eidolon's features are packaged into its subtype, chosen at 1st level alongside its base form. The subtype is like a thematic choice (such as Angel, Demon, or Elemental), unlocking new features when its summoner reaches 4th, 8th, 12th, 16th, and 20th level. The Unchained eidolon then has fewer evolution points to spend on evolutions. There are also some new evolutions, plus re-wordings of evolutions from the original class. The class's Aspect and Greater Aspect class features have been rebalanced accordingly.
Change 2. Rebalanced spell list and spell levels
The APG Summoner can learn and cast spells at lower levels compared to other classes. For example, a 4th level APG Summoner can learn Haste as a 2nd level spell, whereas Haste is a 3rd level spell for other spellcasters, who otherwise must wait until level 5 or later. Therefore the Summoner can cast certain spells earlier and more cheaply than other classes. This also has some odd consequences when determining costs and caster levels of potions and similar items, where spell level and caster level are considered.
With the Unchained Summoner, the spell levels now match the progression of other 2/3 casters, like bard, alchemist, and magus. Examples: Haste is a 3rd level spell (available at class level 7+), Stoneskin is a 4th level spell (available at class level 10+), etc.
Verdict: It depends who you ask
From a player perspective, the Unchained Summoner is weaker than the APG Summoner. Compared to the original, they have fewer resources to spend on their eidolon's evolutions, and they no longer get spells earlier than other classes.
From a GM perspective, the Unchained Summoner is more predictable and easier to manage. The Unchained eidolon is more specialized and less customizable, and the Unchained Summoner's spell progression is closer that of similar spellcasters. I've known several Pathfinder GMs to allow Unchained Summoner only, and ban APG Summoner in their games.