...while with the [interval training] I run out of break quickly and find it hard to continue the jog.
Which one would give me that bit of stamina that I need to keep going in a fight?
As you've seen - interval training is more tiring, and will help more. But, as Sean says neither will contribute very directly to MT performance.
I train MT now but earlier trained in Kyokushin karate for many years in Japan - the best workout I've seen for building endurance for fights is the "big mitt" Kyokushin guys use - random googled indicative video: https://www.youtube.com/watch?v=e8CQ4ZLMSaQ
might be hard to do at lunch time though - you need a pad holder, and a bit of space - preferably private
having someone's body weight behind the pad encourages you to hit hard to actually move them, so front kicks, punches, knees and elbows, side and back kicks, can do a lot of hard work through the target,
you can attack full speed and power (given a similar strength/size mitt holder) in your own rhythms (vs thai pads where you're waiting for your partner to move them around, which has pros and cons but tends to give less workout intensity)
you can throw in low turning kicks more freely and harder than with thai pads.
unlike a heavy bag, the big mitt holder can be moving towards you, circling, backing away, or some combination thereof which affects your technique selection, e.g. you might prefer elbows and knees to break their forward momentum if they close suddenly, and low turning kicks or spinning back/heel kicks if they're circling, gliding side kicks to chase a retreating opponent, stepping-in front kicks or jabs to catch them as they start to close etc.
sometimes we'd do several 2 or 3 minute "rounds" with ~15 second rests, other times we'd do 20-seconds-on / 20-seconds-off high-intensity rounds
big mitts can be hard to find (in Australia at least) and expensive.
So, if you're serious about building stamina for fighting, and can find a mitt and partner, I'd definitely give it a go.