I've been recruiting software engineers for about 15 years now. Lots of problems to mention here.
I'm currently working as the sole web developer of a company for a
year. Out of my desire for a higher pay and a mentor, I started
submitting applications to different companies without my current
employer's knowledge.
If you are the sole web developer of a small company where you have no mentor, it sounds like your current employer is not a great place for you to be as a 22 year old. You have nobody else to learn from and you feel you are underpaid (a notion that was confirmed when you were offered a whopping 70% increase with a new offer). At your age you would generally be better off at a job with a mentor and with co-workers that you could learn from, even if you were making less money.
Last week, I was offered a job in a company with a big development
team (20 developers atm) with a significantly greater pay (almost a
70% increase in gross). Out of excitement and self-interest, I
immediately took the offer and gave my 30-days notice to my current
company.
As a 22 year old getting a 70% increase you should be excited here, but you should be equally excited (from a career development perspective) of your ability to now work with some other people. If you are a good developer, the money will come - the key is honing your craft and getting good at it, and finding dev shops that allow you to learn and grow.
My boss was, of course, really surprised and requested that we finish
all our pending tasks first before I leave.
Their first reaction is always surprise. Even if he/she wasn't surprised, that has to be the initial reaction if a counter offer is to be made. If you had asked any decent recruiter or career expert what would happen after your resignation, they would have predicted the steps that your company made with a high degree of certainty. Any company that is about to make a counter offer first has to act surprised, then say what big things are in store for you (new projects, a promotion you had coming). This is standard fare.
By the end of last week, the company president contacted me personally
and offered to match the other company's offer (though slightly less).
But said that he totally supports my decision should I continue to
leave. But said that the company is on to something big and might
venture into different development projects.
Again, this is pretty standard counter offer stuff here, but usually they match it to the dollar or even go above the other offer. They promise you a more interesting role and responsibility. That doesn't mean that the promise is an empty one, but that is what companies do.
I do not know which side offers better opportunities. I do know that I
owe my current company for giving me my first job. If I do decide to
stay, what do I say to the new company, so that I don't burn bridges
should I decide to ultimately go there because the opportunities in my
company doesn't work out?
It depends on how you define better opportunities. At your age, learning is the most important thing in your career development. As I said, the money will come to you if you get good at your job, so focus on that first and worry about making enough money to maintain a decent lifestyle and pay your bills. I can't see how being the sole web developer at a company, where you were quite obviously grossly underpaid and without a mentor at the impressionable age of 22, is a solid career choice. It may have been your only choice at the time, but it's not an ideal situation.
You say you 'owe' your current company for giving you your first job? It sounds like they were the ones that owed you, as they clearly were underpaying you for at least a portion of your stint. Do you know how long it takes most people to get 70% increases? The fact that this new employer gave you an offer this high, and then your current employer almost matched immediately is a clear sign that you were underpaid. Being loyal to a company is a good thing overall, but being loyal to a company should never come at the expense of your own career and being loyal to yourself (and family that depends on your career success). I feel your loyalty to your current employer may be at your own expense.
You don't need to listen to all the doom and gloom that most recruiter articles will tell you ('You will be the first one fired', 'Your loyalty is always in question now and you'll never get a promotion', etc.), as not all of that is always true. Lesson learned, classic counter offer situation that happens all the time. Judge opportunities on more than just dollars (unless you are in dire need of every dollar), and at 22 you really need to find some people to learn from. Good luck either way!