Read about why I chose the RX100M3 in this post.
The Sony NEX-3N (discontinued, but available used for around $200 or less on eBay) is a great economical alternative to the RX100M3. It has the 180-degree flip up screen and smile shutter just like the RX100M3. However, it does not come with WiFi, Sony apps or an electronic viewfinder (EVF). It has a lower resolution LCD and is bulky enough that it won’t fit comfortably in my jacket pocket (but it will fit). It won’t fit in pants pocket unless you have unusually big pockets. Image quality with the kit lens is slightly worse than the RX100M3. None of these things really bother me except for the bulkiness. The two pictures below show how much bigger the NEX-3N is compared to the RX100M3:
If you don’t mind fixed focal length lenses (no zoom), the 16mm pancake lens (SEL16F28) will help reduce the lens bulk.
If you want more features, the NEX-5R and NEX-5T may be better choices. They are available used only (~$250-$300 on eBay) and come with touchscreen, WiFi, apps, higher resolution LCD, ability to use an infrared (IR) remote and better autofocus. They are similar in size to the NEX-3N. All these cameras come with a 16MP sensor from Sony and has similar image quality, but the additional features of the 5 series lend itself better for more serious photography.
The main advantage of these cameras over the RX100M3 is that the lenses are interchangeable. When paired with a higher quality lens (not the 16-50mm kit lens pictures above), the bigger APS-C sized sensors on these cameras will result in better image quality. If you are looking for a more serious camera that is also somewhat portable, then the NEX-5R or -5T may be good options.
Below is a picture I took with the NEX-5N (an older version of the NEX-5R/5T) with the older 18-55mm kit lens. It was captured in RAW format and processed in Adobe Lightroom:
In short, the additional cost of Rx100M3 is worth it to some (including myself), but not to all. NEX-3N/-5T/-5R is a great cheaper alternative and has an added advantage of allowing interchangeable lenses.