There are three common battery sizes for mech mods: 18650, 18500, 18350. They all operate at 3.7 volts, the primary differences between batteries being capacity (larger ones last longer) and drain (max amperage output). There is different battery chemistry or chemical makeup of these batteries. Pretty much all use Lithium ions, but the ones you want to use are IMR (which use magnesium), as they are far less likely to explode on your face than ICR, and are therefore called "safe chemistry". These are recommended for any mods, but are a must for mechs.
The benefits of mech mods are:
1. The most practical benefit is they allow you to use low-resistance atomizers you have built yourself (RBAs). In regulated mods these are detected as a short and will not fire.
2. They look really nice and have a small form factor (compared to my MVP). They're a bit bigger than Egos but they have greater battery capacity.
3. Another benefit is they are completely mechanical--no wiring, circuts, LCD/LED. The thinking is that there's far less to fail, they're essentially a battery housing with a mechanical switch and 510 threading, so they can last indefinitely.
It is not necessarily true that there is smaller capacity, as the atomizers are a separate topic. RDAs (rebuildable dripping atomizers) are very popular and are a good starting point, but there are rebuildable tank atomizers, some with even more capacity than a Protank or other comparable tanks. Additionally, since they have 510 threading, you can pop your Protanks or any 510 clearomizers on a mech mod. Most won't take Ego threading (with the threads on the outside) though.
The Mech users I have talked to normally have 4-7 fully charged batteries on hand to last thru the day... something to think about. They also go thru 4-8 ml of juice a day too ( the guys I talked to... this is probably not the norm but listening to them it seems to be)
From my experience, this is not necessarily true. I go through 2 batteries/day on a fairly heavy day. Probably use 2-4 mL of juice (which would be about a full Protank or so), and can last a good 12-20 hits after a drip. However I am definitely more conservative with my builds, I run about 1.0-1.2 ohms.