GFs, Espers and Summons are all similar in that they summon a fighter to do damage for you. But here are the differences:

On abilities: GFs offer a wide range of abilities to those equipped with it. Espers offer magic spells and status bonuses for level ups, but that's pretty much it. Finally, Summons offer no abilities.

On accessibility to characters: You have one of most GFs and Espers, but Summons can be Summoned by anyone with enough MP and with the skill of Summoning. This is a major advantage.

On summon costs: GFs cost nothing. Espers and Summons both cost something.

On number of times used: GFs can be used indefinitely as long as the HP stands up (in FF8, that usually is not too much of a consideration, but in FB, where some can quickly deck you while the GF meter is counting down, that weakness can be pretty bad). Furthermore, GFs do cripple the user until the summon is cast. Espers can be cast once at first, a limited amount of times later. Summons can be used indefinitely also, as long as the caster's MP holds up.

In FB, judicious use are made of all of the above. Many new GFs are created, but the Council of Dragons is a Summon. However, there are exceptions to these rules. The most blatant exception is the Overlord. He offers all spells (just like Espers), offers bonuses for level-ups (just like Espers), costs MP (like Espers and Summons), offers some abilities (like GFs), can be used as long as MP holds up (like Espers and GFs), must be equipped but can be cast like a Summon by anyone with the Summoning Ability (taking a page from Summons and Espers/GFs), and so on.