Both those descriptions of gun licensing in Massachusetts are not quite right. I lived there most of my life and had a Class A LTC for most of that time before retiring to gun friendly New Hampshire. Mass is most definitely not a "shall issue" state - the licensing authority, which is the local Chief of Police, has near-total discretion over whether you will be granted an LTC, and which type. (FWIW, "sheriffs" in Massachusetts are county officials who, I believe, only have authority for running prisons and/or transporting prisoners or some such, and of course sucking up tax revenues. They have nothing to do with gun licensing). Some municipalities (not many, thankfully) simply refuse to issue anything at all, others will issue only Class B (restricted to less than 10-round mags, and no CC), and some will issue the coveted Class A but often only after you jump through some hoops. Yes, there is a state-level appellate procedure if your Chief chooses not to issue you a permit, but good luck with that. The only "shall issue" license in Massachusetts is for long guns.
One standard procedure is for a Chief to issue only Class B for your first permit, upgrading to Class A when it's up for renewal in 6 years (licensing fee is $100 each time, BTW). Either way, it's now a state requirement for first-time applicants to take a certified training course and some Chiefs will also require live-fire proficiency testing - not anything that anyone who tunes in here regularly will have a problem with, but it's one more hassle and it takes time. The Chief also has discretionary authority to place additional restrictions on your Class A LTC, such as restricting the hours between which you may carry - most don't do that, thankfully, but they do have that authority. The best thing you can do is to research the situation in the town(s) you're looking to move into and be sure which side of the fence the Chief is on (and then hope the next Chief doesn't have some different policy).
Assuming your Chief is gun-friendly, or at least gun-tolerant, I think a larger issue is the so-called "consumer protection" laws in Mass that essentially prohibit the sale of many handguns. If a manufacturer wants to sell a particular model in Mass, they have to submit 5 of them for destructive testing by the state, and the guns have to pass certain requirements including very heavy trigger pulls, loaded-chamber indicators, etc. Some manufacturers actually make special Massachusetts versions of their guns that will pass the tests, others - Colt, for example - just refuse to knuckle under and that's why you won't find any new Colt handguns for sale in the state. To make matters worse, there's an official "list" but a gun simply being on the list doesn't mean it can be legally sold - there's an additional vague list of requirements that the Attorney General refuses to indicate which guns satisfy, and many retailers live in fear of being prosecuted because of it, so refuse to sell particular models. And, of course, it goes without saying that guns that are no longer manufactured will never be on the list.
And of course, Mass still has the AWB, so for example the only new M4s for sale have pinned stocks, no bayonet lug, etc. (so called "M4gerys"), and only pre-AWB mags larger than 10 rounds can be sold, usually at a premium, or even legally possessed. So forget about that nice new double-stack 13-round 9mm pistol - it'll come with a 10 round "cripple" mag. You might find a used one that's been in the state since 1994, and those mags can legally exceed the 10-round limit, but not new mags. And forget about mail-ordering ammo or even reloading components - even though it's not illegal in Mass, the Attorney General has made it clear to the big mail-order houses that he (it was originally a "he", now a "she") will prosecute anyway and it's not worth their while to defend a lawsuit for the profit they make selling into Mass, so they don't. You can't even have the stuff sent to a friend in NH or VT - they won't sell to you if your credit card billing address is in Mass. And, don't forget, it's illegal to possess ammunition in Mass without a permit, and reloading components are defined as ammunition, so if your kid happens to have a spent piece of brass in his pocket, or you happen to drop a piece or two of brass under the seat of your car and your (unlicensed) wife then goes for a drive, they've both committed felonies.
Yes, there are ways around all this. Most of the serious gun hobbyists in the state cultivate a few FFLs who'll bring in and sell guns that aren't on the "list." And most of us were able to identify a few mail-order houses who either didn't know or didn't care about the AG's threats. But why go through all that hassle if you don't have to? If you already live there, or absolutely need to live there for whatever reason, that's one thing - but I can't imagine any serious gun enthusiast who would choose to move into Mass if they didn't have to.