Will buying a newer mower solve my issue with dying while cutting thicker grass?

I have an older 6.5 hp Toro and it dies frequently going through tall or thick grass. I bought a brand new Toro with a 190cc 7.25 ft/lb. Torque engine and it had the same problem, perhaps more so. If I spend a little more money (about $400 more than the new Toro) and get the Honda HRX217VKA will it make a difference? It also has a 190cc engine but I've read that the Honda engines are much better.

I would think the problem is you are letting the grass get too high between mowings. Instead, move the blades up to their highest setting, mow then go back and drop the blades to desired height. Actually for my fescue lawn I keep the blades at the highest setting as the more leaf surface, the stronger the plant and root system. In the peak growing months… Depending on your grass type, you might mow every 4-5 days instead of 7 days. Then as temps move into less favorable growing, you can drop back to 7 days.

I need to know if the difference between these two mowers will help at all. I realize that cutting the grass more often would solve the problem entirely, but I don't always have time and usually on days when I do have time to mow it ends up raining. So I need something that will hold up a little better than what I have without going to the commercial brands which cost thousands of dollars.