Key systematic differences (by HWalsh a Paizo regular)
1. Character ability point distribution.
In Pathfinder it was very common to want to become "SAD" or Single Ability Dependent. In fact this is why many classes were more highly regarded. One wanted the single highest bonus because those single highest bonuses mattered in so many ways. Characters were generally limited harshly in what they could begin with and as such were forced to hyper prioritize if they wanted to reach optimal, or even near-optimal, levels of performance.
2. Ability point gains.
There were three kinds of ways to raise ability scores in Pathfinder. The first was ability point gains. The second was enhancement bonuses from items. The third was wishes/tomes.
In Pathfinder every 4 levels a character gained 1 ability point. This, over the course of their lifespan, granted them potentially +5 points distributed across their ability point array from levels 1-20.
In Starfinder every 5 levels a character may raise 4 separate ability scores by +2 points (for characters below 17 points) or by +1 point (for characters at 17 points or higher) this allows for potentially 4 raises in a character's life span and the potential addition of up to +32 points.
This allows a much greater flexibility in stats and removes, almost completely, the SAD/MAD comparison. Indeed a character that begins with a stat array of 16, 16, 12, 10, 10, 9 after Race/Theme could gorw:
lvl 05: 18, 18, 14, 12, 10, 09
lvl 10: 18, 18, 16, 14, 12, 11
lvl 15: 18, 18, 18, 16, 14, 13
lvl 20: 18, 18, 18, 18, 16, 15
This is far higher than any character from Pathfinder would have without magical enhancements.
Enhancement bonuses from items are also a major concern. In Pathfinder items were limited only by stacking and wealth. Again, this directed players to compound for the highest bonuses possible. There were a number of ways to enhance bonuses, but the typical ones were as follows:
Enhancement Bonuses, a character could purchase enhancement bonuses of +2, +4, or +6 to an ability score.
Tomes, by reading certain books characters could gain bonuses of +2, +4, or +6 to an ability score.
Wishes, a character could also obtain up to +6 from wishes and other sources. This allowed a character to gain up to +18 to a single ability score.
In Starfinder this is not possible. Characters are limited, at the most, to a single +6 in one score, a single +4 in another, and a single +1 in a final one.
There are no wishes or tomes or other sources that I have found at this time in Starfinder. This lowers overall maximum scores which narrows the gap in power level considerably. Indeed it was very possible in Pathfinder to have a stat start at 20 and then raise to 25 naturally, then be raised in other means to 43.
01st: 18, 14, 11, 10, 10, 10
05th: 19, 16, 13, 12, 10, 10
10th: 20, 18, 15, 14, 10, 10
15th: 21, 19, 17, 16, 10, 10
20th: 22, 20, 18, 18, 10, 10
This character is perfectly functional. Is it optimal? Maybe. That is hard to tell. What we do know about this build, however, is that it will be lacking in other areas. It isn't bad, but the overall benefit from all of this is a grand total of a single +3 over a more balanced character. A +1 at 5th, a +2 at 10th, and a +3 at 20th. While at the same time being a set of +2's behind in other categories. Overall the gain may or may not be worth it.
Regardless the gain is far less pronounced than it would otherwise have been in Pathfinder and can be even worse if a character tries to maximize 2 stats, as it renders it impossible to naturally gain a +5 stat bonus in more than one stat.
In any event, this radically changes ability maximums and how such things should be considered.
2: Dual Role Functionality.
The next important issue to discuss is that every class has dual role functionality in Starfinder. Realistically every class needs a way to fight in both melee and ranged combat. With the possibility for attacks at excessive ranges it is only a natural consideration. Especially when we consider that an entire subsection of the game is fighting in space combat on crew operated vessels. Something that did not exist in Pathfinder as a common play aspect.
3: Skill Distribution.
This is the elephant in the room. Skill distribution is a huge part of Starfinder. Not only do classes have much greater expanded class skill lists, but also the number of distribution points changed radically. In Pathfinder many classes had only 2+ Int modifier in skill points per level, this was compounded by the fact that many of the classes that had this did not have a reason to increase Int as well. This causes some classes, IE Fighter, to dump Intelligence as well, meaning some classes could gain as little as 1 skill point per level. This rendered many characters with few skill options.
In Starfinder every class gains at least 4+ Int modifier in Skills and with the already explained different Ability Point distributions it is easy, without even moderate inconvenience, for the meatiest of meatheads to have +5 - +6 skill points per level by level 15.
This adds a lot of variable paths for characters in both a roleplaying sense (My meat headed warrior also has a habit of studying the cultures of other races, primarily to learn about their weapons and tactics, but learned that he had a deep interest in history as well...) and a raw mechanical sense.
Combat in Starfinder is similar to, but different from, combat in Pathfinder. The Attack of Opportunity tree has been pruned. The action economy has been modified. Full attacks are not as powerful, or as necessary, as they previously were and have drawbacks aside from action economy concerns for example.
One large alteration is that Starfinder characters are far more durable than Pathfinder equivalents. A Fighter in Pathfinder would have HP equal to 10+Con Modifier, +1d10+Con Modifier/Level (typically 6+Con Modifier per level) meaning at a +4 Con at maximum level that class had around 204 HP. This is impressive, but comparatively pathetic compared to the Starfinder equivalent that would typically have 151 HP and 220 SP for a total of 371... This is not taking into account the prevalence of effective health regeneration (force shields) and such that exist as options in the setting.
This is still something I am studying but a combination of lower overall spellcasting levels available to PCs with things such as spell shields and the like as well as a greatly reduced spell list (particularly in the utility area) spellcasting in Starfinder is simply not as effective as it was in Pathfinder. It also is not as easily interrupted.