It's true that most BattleMechs have more guns, though not all. As far as I can tell they don't generally have weapons that can penetrate enemy armor, so this is not an advantage over most forms of mobile suits. They don't need more weapons if they have nore powerful ones. Many mobile suits are quite customizable, there are tons of variants of most common mobile suits. Most mobile suits have thrusters capable of propelling them through the air, not to mention that most can fly either under their own power or through sub-flight systems. A mobile suit can actually turn around much quicker than a BattleMech.
I see the main barriers for the adoption of mobile weapons being logistical and a lack of familiarity with them. Earth's mobile suit production capabilities would not be sufficient to export that many, not to mention maintaining those mobile suits obtained.
They don't make weapons that penetrate armour? Have you seen what a PPC can do?! it's a beam weapon, only more primitive to the gundam ones. Shorter range and slower firing rate, but it packs a hell of a punch. Not buster gun level, but at least on part with average beam weapons. Battletech also has gauss or mac weapons if I'm not mistaken.
On the point of variants for mobile suits.. yeah, that does offer customizability.. but only in the sense you have to have room for another mobile suit for a different weapon set, while say an Atlas can have a few different types of weapons in storage that takes up WAY less space than a whole mech.
So there's pros and cons.. depends on your funds, and combat style.
Now.. as to mobile suit mobility/ability.. yes, many do come with thrusters, flight systems, etc, but many of those are geared for space flight, or a few specific suits with a flight attachment as many aren't meant to fly in an atmosphere. Yes, I know there are some that are, but those are usually spec built to fly, or special units. Most are at most jump capable.
The Battletech ability to rotate at the waist in full 360 adds a new dynamic to movement.. you can still advance on your target, or retreat, while being able to shoot in any direction without losing speed or direction of travel where a mobile suit is usually limited to the movement of a human body. I don't recall any mobile suits that rotate at the waist in full circles. Thus when they turn to shoot something behind them, they full bodily turn and lose speed doing so. But over all, yeah, they can move about faster, generally change direction faster, and can side step far easier than a battlemech, but then comes down to environment on which would be better..
Availability.. mobile suits definitely more rare than battlemechs.. gundanium is rare(r).