OK, so if I'm reading this correctly, your company, within 15 minutes of receiving your resignation, offered to match your new offer, with the additions that:
- You will continue to make your current salary and then get a big end-of-year bonus to make up the salary difference (this isn't a salary increase, it's simply a promise of a bonus, more on this in a moment)
- You will also receive equity in the company
This raises a few flags:
This decision came back in 15 minutes, and the amount of money involved is 50% of your salary. The company is able to spend tens of thousands of dollars in 15 minutes, just because you put in a resignation. This screams to me that the company knows you're being underpaid and simply decided not to tell you or give you the raise you deserved, just because they're cheap and/or greedy (that's the only reason to not pay your people what they're worth when you are able to do so easily). What's to say in another 5 years from now, as inflation (at least in North America) is poised to skyrocket, that you won't find yourself in this same situation again, where your wages have stagnated because your company directors are cheap, greedy, or both?
The end-of-year bonus thing is kind of sketchy. First of all, before you can even reasonably consider this, it absolutely must be in writing, that you will be paid a particular sum on a particular day; there are too many stories of bonuses that are promised but never materialize. So before going forward with even considering this counter-offer, make sure that's in writing. Now, the other problem with this is, the way I read it, you're getting the difference between your current salary and your competing salary, in a lump sum, at the end of the year. The problem is you're being shortchanged. Here's some math:
Let's say you make $240k/yr (just using this to get nice round numbers in the math, ignore the actual numbers here), so 50% of your salary is $120k, which is the amount of the bonus. If this was paid as a salary, it would be paid $10k/mo over 12 months, or it can be paid as a lump-sum at the end of the year.
Now, let's say you are investing your money (which you should be) and not letting it rot in the bank. Let's say you are getting a rate of return of roughly 0.5% per month, which is modest (works out to slightly over 6% per year). Ignoring compound interest for the moment (and this is a BIG deal, but the math is hard so I'm ignoring it to make the math easier), this is what this looks like:
In month 1, you invest $10,000 and get $50.
In month 2, you invest another $10,000 ($20,000 total) and get $100
In month 3, you invest another $10,000 and get $150.
In month 12 you invest another $10,000 and get $600.
The total amount of money in interest you will get is (600 + 50) * 6 = $3900. It's actually more than that due to compound interest, but as I said I'm ignoring that for simplicity. So in order to make the deal "even", your company actually needs to pay you more than the difference, to make up for the fact that they are not giving you the money in a timely manner. In this example case, the amount of the bonus is $120,000 and the amount is roughly $4000, so we're talking a 1/30 increase, but again I am not counting compound interest; the real number is probably closer to 1/20 and that's conservative (it assumes only 6% per year which is very easy; the real number is probably closer to double that if you get a good wealth manager).
So, even accounting for the fact that they are paying you this bonus, and assuming it all goes to plan and they don't try anything fishy, they're still scamming you unless they raise the amount by at least another 5-10%.
Equity means nothing until the company is sold. You should only accept it if you truly believe in the company; if you have any doubt as to the company at all, you should just let it go in one ear and out the other and don't even consider it. You may want to ask for company financials to inform you better on this point, but even knowing the company financials only tells you that your equity isn't worth actual zero; it doesn't tell you positively that it's worth anything. So don't even worry about this.
The other issue with the bonus is that it might disqualify you (not legally, but de-facto) from receiving an additional bonus. Like, say that annual bonus time comes around, you worked your ass off, everyone gets their bonuses, and you get jack. You say, "Where's my bonus? I worked my ass off". Management comes back to you and says, "Oh, we gave you your bonus, as we agreed, that's your bonus thanks for your hard work". How would that make you feel? You know this company has a culture of broken promises, so why would this be different?
Even if you could resolve all of the above problems, is money really even the issue here? Would you stay at this company if they simply paid you more? The issues you raised, e.g. boredom, desire to broaden your horizons, and broken promises, are not issues that are easily solved with money. Is money even the issue at all?