That depends entirely upon your individual needs and style. The general operation of each is the same for the most part. Both offer unique advantages between each other though.
The 510 can be obtained in a color pattern that closely resembles a real cigarette. It's size is relatively realistic and they are available with LED colors (orange or red) that simulate the burning end of a cigarette.
The 510 is available with several types of PCCs (Personal Charging Cases) which resemble a cigarette pack in size. These help make up for some of the 510s downsides (i.e., battery life).
The 510 has a battery usage time which varies depending upon the user, but generally lasts for around an hour to three hours of use.
The 510 is available with longer
batteries that offer longer usage times between recharges and longer/higher capacity carts and attys. 510 cartomizers are also available in various styles which replace the usual cart/atty section of the 510 with an all-in-one unit.
The eGo or Fat Batts 510 models (Riva, Tornado, etc), are larger and do not resemble a real cigarette. They are compatible with 510 attys and are also capable of utilizing eGo proprietary carts/attys and cartomizers.
The eGo offers a significantly longer battery life with longer usage time before recharging becomes necessary. Usage times have varies (depending on the mah of the model) from 6 to as long as 18 hours depending on use. The Joye versions are available in 650mah, 900mah, and 1000 mah. Other makes have even higher mah ratings.
The eGo is able to use eGo XL attys/carts in cylinder or cone shaped, or XL eGo cartomizers, all of which add a substantially higher
juice capacity (1.5mls to 2.5mls depending on model). This means less refilling and more usage before needing to refill.
Both eGo and 510 models are available with a pass-through option. These are batteries that come with USB cables and are able to be used while connected to a USB power source. Some are also capable of being used with the cable detached.
Both models are available in auto or manual battery types. Both are available in a wide range of color options. Both are considered to be reliable and well made in general. Both have a wide range of accessories to suit your needs, i.e. PCCs, drip tips, cases, etc. Both are available from a wide range of manufacturers and retailers. Some will be better made than others, but it is always a good practice to search for
reviews and opinions regarding whichever make, model, or manufacturer you choose before buying.