Hollows
Hollows are the spirits of pluses that were not given the soul burial by a Shinigami before their soul chain disintegrated. Hollows have a number of stages of power that are listed in the "Tier System" post. Frankly, their powers are rather basic, being always active. Hollow must consume each other to grow in power. Each one has a mask and a Hollow hole, and their body is usually completely changed from their living form, usually to be better suited to fighting and consuming their fellow Hollows.
Racial Abilities
Hollow have very little in common when it comes to powers. There are almost no universal hollow abilities save one: the Cero. Cero are concentrated balls of energy that are launched at opponents. These can be slightly customized, but the basic Cero is nearly all a Hollow has access to.
Basic Powers
Hollows have no structure to their powers. They are always active and are often integrated into their bodies.
Pros
Hollows are bigger and stronger than most of their opponents of the same tier. The nature of their power gives them ultimate freedom with it.
Cons
Generally Hollows' powers are less powerful and there are less of them. And frankly, they just aren't as cool as Arrancar. So...
Arrancar
Arrancar are a form of Hollow that have removed their masks and forced themselves into a more human form. Each Arrancar has a mask fragment and a hollow hole somewhere on their body. Arrancar did exist before Aizen forced Shinigamification, but they were few and far between. The creation of Arrancar has continued to flourish even after the death of Aizen and the entire Espada.
Racial Powers
Cero: Just like the Hollows, Arrancar can all use Cero. Unlike the Hollows, though, Arrancar have a much greater freedom to customize the Cero they use. Among the number of specialized Cero, a few important ones stand out:
Bala: A condensed, less powerful version. It moves much faster than the Cero but does considerably less damage
Gran Rey: A Cero that can only be performed by members of the Espada. It requires the user to mix their blood with the Cero, and each Espada has a custom color for it. Upon impact, it begins to spin and disrupt space and time.
Cero Oscuras: A Cero that converts light into deadly darkness. It can be used only by Espada and is one of the most powerful Cero in existence.
Sonido: Basicly the Arrancar's equivalent to the Shinigami's Shunpo technique. The only real difference is that it makes a sort of "white noise" sound when in use, as opposed to the swishing sound of Shunpo.
Pesquisa: Spanish for "Inquiry," Japanese for "Probe Circuit") is the Arrancar equivalent of the Shinigami ability to sense Spiritual Pressure. It functions very similarly to sonar.
Hierro: refers to the hardened skin of the Arrancar, which is a result of their compressed spiritual power. While their skin is strong enough to block even released Zanpakutō bare-handed, it is by no means impenetrable. Stronger Arrancar generally have proportionally stronger skin than usual.
Garganta: How Arrancar and Menos-class Hollows move to and from Hueco Mundo. Kaname Tōsen, Kisuke Urahara and Mayuri Kurotsuchi have also demonstrated the ability to use the technique. It literally tears open the dimensional fabric separating the worlds, revealing a tunnel of whirling, torrential energy that must be focused and solidified to create a discernible pathway.
Zanpakutou: Just like the Shinigami, Arrancar carry Zanpakutou. However, their Zanpakutou serve a different purpose. When evolving into Arrancar, Hollows seal their powers and form into the shape of a blade. Due the the fact that Arrancar's Zanpakutous are basically secondary bodies, they have more freedom than Shinigami as to the shape of their Zanpakutou.
First Stage
Resurreccion: This is similar to the Shinigami's Shikai. In Resurreccion form, the Espada unseals his or her Adjuncas form from the blade, thereby accessing their former powers, though usually more powerful. This usually involves the physical change of the body and the disappearance of the Zanpakutou. Basicly, the Resurreccion form of and Arrancar is as if they had evolved a non-Shinigamified step above the Adjuncas form, which is otherwise impossible.
Second Stage
Resurrección Segunda: Just like the other races, some Arrancar have a very rare second stage of powers. This involves limiting your full powers even within Resurrección form. This is the final form of the Arrancar and generally makes them much more powerful. The transformation tends to be somewhat animal-like.
Pros
Arrancar generally have a large amount of both abilities and freedom in the use. They are also considerably more powerful than basic Shinigami or Shinobi, their Resurrección generally agreed to be on the power level of a Bankai. Resurrección Segunda are about equivilant to Full Vizard or Full Jinchuriki form.
Cons
Arrancar have a very strict hierarchy. And the power means considerable competition between peers. Arrancar are also not as proportionally fast as Shinigami or Shinobi.