While LTE and 4G will enable you to go even faster, networks still have to enable the faster speeds and the mobile phone have to have a network chip inside that is capable of those speeds. Even if this is all enabled, there are still reasons why you may opt for a 3G Phone. First, if you are primarily using your phone just for the voice service and rarely for internet, then there's less of a reason for your to pay for the higher speeds. 3G plans are usually cheaper than it's superseders, which make them a great option for someone on a budget. Also, if you live in an area that doesn't receive 4G coverage, there's no advantage to a 4G phone. You will actually end up having battery life issues if you don't disable 4G LTE with an LTE phone. If you do decide on a 3G phone, be sure to get the fastest phone available. On Verizon and Sprint, that means you'll want to check that it supports "EVDO REV A." And on AT&T and T-Mobile, look for the highest class of HSPA+ possible (i.e. if not 42 or 21, then 14.4).
When buying a smartphone, it is important to understand that often your speed will also depend on the speed and capabilities of your network. While LTE may be 10 times faster than 4G, the actual speed will depend on your signal strength and network load.
Both 2G and 3G were designed to be primarily used for voice calls, 4G is primarily designed for data transmission. For example, 4G's faster data speeds will allow you to stream videos with higher resolution and less stuttering, play multiplayer games more efficiently and conduct video conference calls. When attempting to load data on similar network capabilities, the speed differences between LTE, 4G, and 3G can be quite noticeable.